Concept explainers
Case summary:
CC Company develops two kinds of kitchen and bathroom cabinets. There are two variants of cabinets:one is a variation of a standard design and is made to order, another is a low-priced line and is made to stock.
The company has been in business for many years and is doing well. The meeting was about the financial status of the company. The meeting was aimed at addressing the operational inefficiency.
To determine:If additional overtime is needed. If so, how much is needed.
Introduction:
Linear programming:
Linear programming is a mathematical modeling method where a linear function is maximized or minimized taking the various constraints present in the problem into consideration. It is useful in making quantitative decisions in business planning.
Want to see the full answer?
Check out a sample textbook solutionChapter 19 Solutions
OPERATIONS MANAGEMENT W/ CNCT+
- 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%.arrow_forwardThe 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.arrow_forwardA goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.arrow_forward
- RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 25 ton of material 1 and 35 of material 3. A ton of solvent base is a mixture of 12 ton of material 1, 15 ton of material 2, and 310 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: RAW MATERIAL Amount Available for Production Material 1 20 Tons Material 2 5…arrow_forward1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?arrow_forwardThe Big Bang Novelty Company (BBNC) makes 3 types of noise?makers: Toot, Wheet, and Honk. A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 20 minutes, has two feathers, and is sprinkled with 0.5 ounces of sequin powder. The Honk requires 30 minutes, three feathers, and 1 ounce of sequin powder. The unit profits are $0.45 per Toot, $0.55 per Wheet, and $0.70 per Honk. The following resources are available: 80 hours of labor, 360 feathers, and 90 ounces of sequin powder. BBNC would like to maximize the overall profit from the noise-makers. (a) Write the linear programming model. Express labor time in minutes in LP formulationb) Solve using Excel Solver. How much of the resources (labor, feathers, and sequin powder) will be used by the optimal solution? If the availability of labor increases by 10 hours, what is the optimal total profit? If the unit profit of Wheet is actually only $0.30 instead of $0.55, will this change the solution? How many of each…arrow_forward
- Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.arrow_forwardA manufacturing fi rm has discontinued production of a certain unprofi table product line.Considerable excess production capacity was created as a result. Management is consideringdevoting this excess capacity to one or more of three products: X1, X2, and X3.Machine hours required per unit areProductMachine Type X1 X2 X3Milling machine 8 2 3Lathe 4 3 0Grinder 2 0 1The available time in machine hours per week isMachine Hours per WeekMilling machines 800Lathes 480Grinders 320The salespeople estimate they can sell all the units of X1 and X2 that can be made. Butthe sales potential of X3 is 80 units per week maximum.Unit profi ts for the three products areUnit ProfitsX1 $20X2 6X3 8a. Set up the equations that can be solved to maximize the profi t per week.b. Solve these equations using the Excel Solver.c. What is the optimal solution? How many of each product should be made, and whatshould the resultant profi t be?d. What is this situation with respect to the machine groups? Would they…arrow_forwardCalvin Butterball is chief of operations for the Fly-by-Night Aircraft Corp. He is responsible for the manufacturing of the company's two models of planes: The parrot and the eagle. Each department of the company has restrictions concerning the number of planes, which can be manufactures each day. No more than 7 eagles and no more than 11 parrots can be manufactured per day. No more than 12 total planes total can be shipped per day. The number of eagles manufactures must be no more than twice the number of parrots manufactured each day. You much use more than 1000 hours of labor per day; it takes 100 man-hours to manufacture each parrot and 200 man-hours to manufacture each eagle. Fly-by-Night makes a profit of $300 per parrot and $200 per eagle. How many eagles and how many parrots should e produced per day to give the greatest feasible profit and to determine the profit?arrow_forward
- 2. A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans require 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earn $800 profit, and a lot of large-size cans earn $900 profit. In order to fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can (and) in order to maximize profit. 8. In Problem 2, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?arrow_forwardDon't use chatgpt, I will 5 upvotes Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1/2 cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of blueberry muffins and y represent the number of bran muffins Alan bakes.arrow_forward009. from: small and medium. There are two flavors to choose from: chocolate and strawberry. There are two toppings to choose from: cherries and nuts. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions. Size small medium Flavor chocolate strawberry chocolate strawberry (a) How many outcomes are there? 8 outcome(s) Topping cherries nuts cherries nuts cherries nuts cherries nuts Outcome (small, chocolate, cherries) (small, chocolate, nuts) (small, strawberry, cherries) (small, strawberry, nuts) (medium, chocolate, cherries) (medium, chocolate, nuts) (medium, strawberry, cherries) (medium, strawberry, nuts) (b) How many outcomes do not have chocolate ice cream being chosen? outcome(s) (c) How many outcomes have both strawberry ice cream and cherries being chosen? outcome(s)arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,