Given below is an LP for a furniture manufacturing company. Maximize Z= 5 x, + 6 x, (profit, RM) 2 x, +x, < 120 (labour, hr) 2 x, + 3 x, < 240 (wood, meter) Subject to: X, x, > 0 Based on the sensitivity analysis results obtained using Excel Solver for the above LP model, answer questions (a) to (c). Variable Cells Final Reduced Objective Allowable Allowable Cll Name Value Cost Coefficient Increase Decrease $B$10 X1 = 30 5 7 1 $B$11 X2 = 60 1.5 3.5 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$6 Constraint 1 Usage 120 0.75 120 120 40 $E$7 Constraint 2 Usage 240 1.75 240 120 120 a) At the optimal solution, how much labour hours was utilized? b) Suppose that the available wood is increased by 50%, what will happen to the optimal solution? c) Suppose that the manager receives an offer from a supplier to get 5 meter of wood at the cost of RM2.50 per meter, should he/she take the offer? Justify your answer.
Q: Consider the following LP problem developed at •• B.9 Zafar Malik's Carbondale, Illinois, optical…
A: In order to solve the problem graphically, convert inequalities to equality for the constraints.…
Q: Teacher Required Penalty History 35 $26,000 Science 30 $30,000 Math 40 $28,000 English 32 $24,000
A: Formulate Goal programming (GP) model as mentioned below- Decision variables: Let x1, x2, x3, x4,…
Q: A firm wants to determine its production rate over the next twelve months. expected demand for its…
A: Decision Variable: Suppose Pi = Production in month-i for i=1,2,3...,12 Si = Shortage in month-i…
Q: A large sporting goods store is placing an order for bicycles with its supplier. Four models can…
A: Objective Functions and Constraints: Based on the given details, the objective…
Q: Dr. Thompson’s sporting goods store is placing an order for scooters with its supplier. Four models…
A: Given data, Scooter are sold = 30,25,22,20 Store space= 500feet Assembly time = 1200 hours…
Q: Explain why it is problematic to include a constraint such as the following in an LP model for a…
A: Linear programming:It is a mathematical model where a linear function is maximized or minimized…
Q: Dr. Thompson’s sporting goods store is placing an order for scooters with its supplier. Four models…
A: Given data, Store Space = 500ft Assembly Time = 1200 hours Boys and girls scooter = 4 hours of…
Q: Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in…
A: Hi, we are supposed to answer three subparts at a time. Since you have not mentioned which subpart…
Q: The optimal value of the objective function using graphical procedures is found by. Select one: O a…
A: Explanation : The feasible solution region on the graph is one which is satisfied by all…
Q: A market analyst working for a small appliance manufacturer finds that if the firm produces and…
A: Answer (a) When given a graph of a profit equation with the number of items produced on the x-axis…
Q: Max 1W + 1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 S 4,400 S 2,240 S 1,600 oz of whole tomatoes oz…
A: Objective of the problem is to maximize profit. Each jar is of 10 ounces. Western Food Salsa (W)…
Q: Kilgore's Dell is a small delicatessen located near a major university. Kilgore's does a large…
A: a. Let W = # of servings of Wimpy to make Let D = # of servings of Dial 911 to make…
Q: Dr. Thompson’s sporting goods store is placing an order for scooters with its supplier. Four models…
A: Given data, Scooter sold = 30,25,22,20 Area of store 500 Assembly time = 1200 Boys and girls…
Q: A large sporting goods store is placing an order for bicycles with its supplier. Four models can be…
A: Linear programming or LP is one of the most simplistic methods to achieve optimization. It assists…
Q: Maximizing Profit Johnson's Household Products has a division that produces two sizes of bar soap.…
A: The retail price of the 3.5-oz size bar soaps is p $ per 100 The retail price of the 5-oz size bar…
Q: Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged…
A: Based on the data given, we understand it is a Linear Programming Problem. The decision variables…
Q: Which one of the following would be a valid objective function for linear programming? OA. Min7XY O…
A: The objective function in linear programming problems (LPP ) is the fundamental-valued function…
Q: 1.) Objective Function: Maximize Z = 60X₁ +50X₂ Subject to Assembly 4X₁ +…
A: Since you have submitted multiple questions, as per guidelines we have answered the first question…
Q: You are given the tableau shown in Table 74 for a maximization problem. Give conditions on the…
A:
Q: Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in…
A: since we only answer up to 3 subparts, we'll answer the first 3 . please resubmit the question and…
Q: w = 4y, +8y2 subject to: 6y +Y2 260 15y, +y2 2 105 Y20, y2 20 Use the simplex method to solve.…
A: Given LP- MIN W = 4y1 +8y2Subject to constraint-6y1+ y2≥6015y1+ y2≥105y1≥0 , y2≥0
Q: Tom's, Inc., produces various Mexican food products and sells them to Western Foods, a chain of…
A: As per Bartleby guidelines, we can only solve the first three subparts of one question at a…
Q: RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production…
A: Let Fuel Additive = F and solvent base = S maximize Z = 2000 F + 1500 S subject to 2/6 F +…
Q: You have been assigned to develop a model that can be used to schedule the nurses working in a…
A: a.) The details that we would collect as inputs to our model are as follows: The shifts or timings…
Q: During the next four months, a customer requires,respectively, 500, 650, 1000, and 700 units of…
A: Cost is one of the most important elements of any organization. The organization produces goods and…
Q: The cost per day of running a hospital is 200,000 +0.5x2 dollars, where x is the number of patients…
A: Given: 1. Cost per day for the hospital is of the form 200,000+0.5x² patients where x is the number…
Q: Kilgore’s Deli is a small delicatessen located near a major university. Kilgore does a large walk-in…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
Q: Dr. Thompson’s sporting goods store is placing an order for scooters with its supplier. Four models…
A: Given Information: It is given that store would like to place an order for at least 275 scooters
Q: Write in normal form and solve by the simplex method, assuming x, to be nonnegative. 1. The owner of…
A: Objective Functions and Constraints: Based on the given details, the objective…
Q: GM manufactures bikini swimming suits. Their business is highly seasonal, with expected demands…
A: LPP FORMULATION Let's define the variables first, let x1 be the total volume of suits (in dozens) to…
Q: Use Excel to solve the linear program, optimal solution and objective function value. A political…
A: S = Number of small signs placed by the roadside L = Number of large signs placed by the roadside B…
Q: If the profit generated per cabinet is P80 and per dresser is P100, write the objecti that best…
A: Linear programming is a process to reach the best outcome such as maximum profit or lowest cost in a…
Q: Implement the linear optimization model and find an optimal solution. Interpret the optimal…
A: THE ANSWER IS AS BELOW:
Q: An investor is looking to invest R 250,000 with the intent of getting the highest possible return.…
A: Given data is Available amount to invest = R 250,000 Limit to invest in ASBA stock = less than or…
Q: Arthur and Son P.A. is an auditing firm that conducts both financial and operational audits. Arthur…
A: Profit from each FA has averaged = $720 Profit from each OA has averaged = $650 Handling capacity =…
Q: In the spreadsheet model shown below, an analyst makes the following data entries. Cell ВЗ В4 В5 B6…
A: Find the Given details below: Given details: Cell B3 B4 B5 B6 Value 113000 90000 119000…
Q: The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each…
A: Answer:Introduction:The given problem is solved using linear programming. The given problem is…
Q: gelleratng a IS following function: H(P) = 120 +9.3 P + 0.0025 P² MJ/h This unit has a minimum…
A: Solution - Brief Introduction with Operating Profit and Loss…
Q: Given the soft constraint X, + X2 +d* - d" = 45, which was originally the hard constraint X, + X2 =…
A: Slack and surplus variables are referred to as Deviational Variables (di — and di +) in general…
Q: Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given…
A: Maximize: 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0
Q: Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the…
A: (a)The objective of this problem is to meet the production demands at minimum cost.The decision…
Q: An appliance manufacturer produces two models of microwave ovens: H and W. Both modelsrequire…
A: Given Information: Oven – H Oven-W Total Fabrication (hours) 4 2 600…
Q: Using the Solver Function in Excel to calculate the following: The main challenge is to allocate no…
A: Given data, Table Blind Average Pot House Intake Pots Per Hour Hourly Expense Min Hours Max Hrs.…
Q: company operates a farm on which sheep are raised. The farm manager has determined that for the…
A:
Q: Use the simplex method to solve the linear programming problem. z= 8x1 - 7x2 + 2x3 X2 + 8x3 < 48 4x1…
A:
Q: A LP model is given as Min z = 30x1+7x2 S/t 12x1 + 3x2 > 32 (High income wor 4x1 + 9x2 > 16 (High…
A: Variables: x1= Number of comedy Spotsx2= Number of Football Spots Objective: Minimize the cost…
Q: A company produces three types of items. A singlemachine is used to produce the three items on a…
A:
Q: Use the two-stage method to solve. Find x, 20 and x, 2 0 such that X1 + 2x2 s 22 X1 + 3x2 2 10 2x1 +…
A:
Q: A company produces two types of transformer. If X1 is the number of type-A transformers and X2 is…
A: Given that: Profit = 924 x1(Type A) = 32 x2(Type B) = ?
Q: rocess is a good alternat
A: The term "alpha" refers to the difference between the return on investment and the return on an…
Step by step
Solved in 4 steps with 2 images
- Suppose that GLC earns a 2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLCs cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then purchase a car every five yearsduring year 6, year 11, and so on. For simplicity, we assume that Hundo is GLCs only competitor. We also assume that if the consumer is satisfied with the car she purchases, she will buy her next car from the same company, but if she is not satisfied, she will buy her next car from the other company. Hundo produces cars that satisfy 80% of its customers. Currently, GLC produces cars that also satisfy 80% of its customers. Consider a customer whose first car is a GLC car. If profits are discounted at 10% annually, use simulation to estimate the value of this customer to GLC. Also estimate the value of a customer to GLC if it can raise its customer satisfaction rating to 85%, to 90%, or to 95%. You can interpret the satisfaction value as the probability that a customer will not switch companies.The eTech Company is a fairly recent entry in the electronic device area. The company competes with Apple. Samsung, and other well-known companies in the manufacturing and sales of personal handheld devices. Although eTech recognizes that it is a niche player and will likely remain so in the foreseeable future, it is trying to increase its current small market share in this huge competitive market. Jim Simons, VP of Production, and Catherine Dolans, VP of Marketing, have been discussing the possible addition of a new product to the companys current (rather limited) product line. The tentative name for this new product is ePlayerX. Jim and Catherine agree that the ePlayerX, which will feature a sleeker design and more memory, is necessary to compete successfully with the big boys, but they are also worried that the ePlayerX could cannibalize sales of their existing productsand that it could even detract from their bottom line. They must eventually decide how much to spend to develop and manufacture the ePlayerX and how aggressively to market it. Depending on these decisions, they must forecast demand for the ePlayerX, as well as sales for their existing products. They also realize that Apple. Samsung, and the other big players are not standing still. These competitors could introduce their own new products, which could have very negative effects on demand for the ePlayerX. The expected timeline for the ePlayerX is that development will take no more than a year to complete and that the product will be introduced in the market a year from now. Jim and Catherine are aware that there are lots of decisions to make and lots of uncertainties involved, but they need to start somewhere. To this end. Jim and Catherine have decided to base their decisions on a planning horizon of four years, including the development year. They realize that the personal handheld device market is very fluid, with updates to existing products occurring almost continuously. However, they believe they can include such considerations into their cost, revenue, and demand estimates, and that a four-year planning horizon makes sense. In addition, they have identified the following problem parameters. (In this first pass, all distinctions are binary: low-end or high-end, small-effect or large-effect, and so on.) In the absence of cannibalization, the sales of existing eTech products are expected to produce year I net revenues of 10 million, and the forecast of the annual increase in net revenues is 2%. The ePIayerX will be developed as either a low-end or a high-end product, with corresponding fixed development costs (1.5 million or 2.5 million), variable manufacturing costs ( 100 or 200). and selling prices (150 or 300). The fixed development cost is incurred now, at the beginning of year I, and the variable cost and selling price are assumed to remain constant throughout the planning horizon. The new product will be marketed either mildly aggressively or very aggressively, with corresponding costs. The costs of a mildly aggressive marketing campaign are 1.5 million in year 1 and 0.5 million annually in years 2 to 4. For a very aggressive campaign, these costs increase to 3.5 million and 1.5 million, respectively. (These marketing costs are not part of the variable cost mentioned in the previous bullet; they are separate.) Depending on whether the ePlayerX is a low-end or high-end produce the level of the ePlayerXs cannibalization rate of existing eTech products will be either low (10%) or high (20%). Each cannibalization rate affects only sales of existing products in years 2 to 4, not year I sales. For example, if the cannibalization rate is 10%, then sales of existing products in each of years 2 to 4 will be 10% below their projected values without cannibalization. A base case forecast of demand for the ePlayerX is that in its first year on the market, year 2, demand will be for 100,000 units, and then demand will increase by 5% annually in years 3 and 4. This base forecast is based on a low-end version of the ePlayerX and mildly aggressive marketing. It will be adjusted for a high-end will product, aggressive marketing, and competitor behavior. The adjustments with no competing product appear in Table 2.3. The adjustments with a competing product appear in Table 2.4. Each adjustment is to demand for the ePlayerX in each of years 2 to 4. For example, if the adjustment is 10%, then demand in each of years 2 to 4 will be 10% lower than it would have been in the base case. Demand and units sold are the samethat is, eTech will produce exactly what its customers demand so that no inventory or backorders will occur. Table 2.3 Demand Adjustments When No Competing Product Is Introduced Table 2.4 Demand Adjustments When a Competing Product Is Introduced Because Jim and Catherine are approaching the day when they will be sharing their plans with other company executives, they have asked you to prepare an Excel spreadsheet model that will answer the many what-if questions they expect to be asked. Specifically, they have asked you to do the following: You should enter all of the given data in an inputs section with clear labeling and appropriate number formatting. If you believe that any explanations are required, you can enter them in text boxes or cell comments. In this section and in the rest of the model, all monetary values (other than the variable cost and the selling price) should be expressed in millions of dollars, and all demands for the ePlayerX should be expressed in thousands of units. You should have a scenario section that contains a 0/1 variable for each of the binary options discussed here. For example, one of these should be 0 if the low-end product is chosen and it should be 1 if the high-end product is chosen. You should have a parameters section that contains the values of the various parameters listed in the case, depending on the values of the 0/1 variables in the previous bullet For example, the fixed development cost will be 1.5 million or 2.5 million depending on whether the 0/1 variable in the previous bullet is 0 or 1, and this can be calculated with a simple IF formula. You can decide how to implement the IF logic for the various parameters. You should have a cash flows section that calculates the annual cash flows for the four-year period. These cash flows include the net revenues from existing products, the marketing costs for ePlayerX, and the net revenues for sales of ePlayerX (To calculate these latter values, it will help to have a row for annual units sold of ePlayerX.) The cash flows should also include depreciation on the fixed development cost, calculated on a straight-line four-year basis (that is. 25% of the cost in each of the four years). Then, these annual revenues/costs should be summed for each year to get net cash flow before taxes, taxes should be calculated using a 32% tax rate, and taxes should be subtracted and depreciation should be added back in to get net cash flows after taxes. (The point is that depreciation is first subtracted, because it is not taxed, but then it is added back in after taxes have been calculated.) You should calculate the company's NPV for the four-year horizon using a discount rate of 10%. You can assume that the fixed development cost is incurred now. so that it is not discounted, and that all other costs and revenues are incurred at the ends of the respective years. You should accompany all of this with a line chart with three series: annual net revenues from existing products; annual marketing costs for ePlayerX; and annual net revenues from sales of ePlayerX. Once all of this is completed. Jim and Catherine will have a powerful tool for presentation purposes. By adjusting the 0/1 scenario variables, their audience will be able to see immediately, both numerically and graphically, the financial consequences of various scenarios.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
- Based on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity that each salesperson will sell 0, 5000, or 50,000 worth of brushes. The probability of each sales amount depends on the effort level as described in the file P07_71.xlsx. If a salesperson is paid w dollars, he or she regards this as a benefit of w1/2 units. In addition, low effort costs the salesperson 0 benefit units, whereas high effort costs 50 benefit units. If a salesperson were to quit Fuller and work elsewhere, he or she could earn a benefit of 20 units. Fuller wants all salespeople to put forth a high level of effort. The question is how to minimize the cost of encouraging them to do so. The company cannot observe the level of effort put forth by a salesperson, but it can observe the size of his or her sales. Thus, the wage paid to the salesperson is completely determined by the size of the sale. This means that Fuller must determine w0, the wage paid for sales of 0; w5000, the wage paid for sales of 5000; and w50,000, the wage paid for sales of 50,000. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Determine how to minimize the expected cost of ensuring that all salespeople put forth high effort. (This problem is an example of agency theory.)The method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whether the home team wins. Then from the proposed ratings, you predict whether the home team will win. (You predict the home team will win if the home team advantage plus the home teams rating is greater than the visitor teams rating.) You want the ratings such that the number of predictions that match the actual outcomes is maximized. Try modeling this. Do you run into difficulties? (Remember that Solver doesnt like IF functions.) EXAMPLE 7.8 RATING NFL TEAMS9 We obtained the results of the 256 regular-season NFL games from the 2015 season (the 2016 season was still ongoing as we wrote this) and entered the data into a spreadsheet, shown at the bottom of Figure 7.38. See the file NFL Ratings Finished.xlsx. (Some of these results are hidden in Figure 7.38 to conserve space.) The teams are indexed 1 to 32, as shown at the top of the sheet. For example, team 1 is Arizona, team 2 is Atlanta, and so on. The first game entered (row 6) is team 19 New England versus team 25 Pittsburgh, played at New England. New England won the game by a score of 28 to 21, and the point spread (home team score minus visitor team score) is calculated in column J. A positive point spread in column J means that the home team won; a negative point spread indicates that the visiting team won. The goal is to determine a set of ratings for the 32 NFL teams that most accurately predicts the actual outcomes of the games played.Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modelled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. (The mean in this example is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (In this example, it is 3(10=17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10). These arguments are the mean and standard deviation of the distribution. Rework Example 10.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example? a. Gamma distribution with parameters 2 and 85 b. Gamma distribution with parameters 5 and 35 c. Lognormal distribution with mean 170 and standard deviation 60
- Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors: The fixed cost of developing the Racer is triangularly distributed with parameters 3, 4, and 5, all in billions. Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000. The selling price in year 1 is 25,000. The year 2 selling price will be 1.05[year 1 price + 50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50( 10)] = 25,725. Similarly, the year 3 price will be 1.05[year 2 price + 50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales. The variable cost in year 1 is triangularly distributed with parameters 10,000, 12,000, and 15,000, and it is assumed to increase by 5% each year. Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.