A company manufactures two products. If it charges price pi for product i, it can sell qi units of product i,where q1 = 60−3p1 +p2 and q2 = 80−2p2 +p1. It costs $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of each product should the company produce, and what prices should it charge, to maximize its profit?
Q: A company produces and sells luxury goods and is able to control the demand for the product by…
A: A company produces and sells luxury goods and can control the demand for the product by varying the…
Q: A "What-If" analysis: A department store sells two popular models of wireless headphones, model A…
A: As per the given information, the excel formulas will be as follows.
Q: A firm offers three different prices on its products, depending upon the quantity purchased. Since…
A: Decision variables - x11= product 1 with a profit of $18 per unit x12= product 1 with a profit of…
Q: A university has three professors who each teach four courses per year. Each year, four sections of…
A: A Small Introduction about Production Management Production management alludes to the method…
Q: How many units of each type should the firm buy in order to maximize total return?
A: The given problem is: Maximize z=400x+800y Subject to x2+y2−4x−6y=67 Using Lagrange multipliers,
Q: The ELC Corporation manufactures two industrial-sized electrical devices: generators and…
A:
Q: A company is considering two insurance plans with the following types of coverage and premiums Plan…
A: Given that: Total coverage for fire/theft insurance = $6,36,000 Total coverage for liability…
Q: Producers of a certain brand of refrigerator will make 4000 refrigerators available when the unit…
A: The step by step solution of the same is as follows:
Q: Lina wants to take a nice vacation trip, so she begins setting aside P250 per month. If she deposits…
A: Given that: a1= 250 rate = 6% t =10 n= 12 ....compunded monthly
Q: The input-output curve of a gas-fired generating unit is approximated by the following function: 4.2…
A: Input-output curve function: H(P)=120+9.3P+0.0025P2 MJ/h Minimum output = 200 MW Maximum output =…
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: Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged…
A: Linear programming problem: Max 6x1 + 10x2 + 8x3 s.t 2x1 + x2 + 3x3 <= 180 2x1 + 6x2 + 4x3 = 240…
Q: The ELC Corporation manufactures two industrial-sized electrical devices: generators and…
A: As per Bartleby's guidelines, I have Solved the first question as multiple questions are asked…
Q: In robust optimization, what is meant by the term "hard constraint"?
A: There are two types of constraints soft constraint and hard constraint. Robust optimization relates…
Q: A train track runs through a rancher's land. Each time a train runs on the track, it causes one of…
A: Since you have posted a question with multiple sub-parts, we will solve the first three for you. If…
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: steel company has two mills. Mill 1 costs $70,000 per day to operate, and it can produce 400 tons of…
A: Cost refers to an expenditure or expenses incurred by an organization in order to produce and sell…
Q: You own a coffee shop in a metro Toronto shopping mall. It is Friday evening and you are trying to…
A: We have to find the value of payoff for quality baked(Q)+demand(D) by using below formula
Q: A company operates under hard budget constraints and has a WACC of 12%. In the current year it can…
A: Below is the solution:-
Q: Drawthe budget constraint for a consumer with standard preferences.
A: For the First Part here is the solution: If the consumer had an income of $3,000 and the cost of…
Q: One company produces two models of calculators on two different floors. In one day, plant A can…
A: Let; A be the number of calculators produced by plant A B be the number of calculators produced by…
Q: Bhavika Investments, a group of financial advisors and retirement planners, is providing advice on…
A: Let, S = dollars invested in the stock fund M= dollars invested in money market fund
Q: A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home…
A: Given, Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56…
Q: Vladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match…
A:
Q: Susan Solomon has been thinking about starting her own fuel station, but Susan's problem is to…
A: Given data:
Q: Blair & Rosen, Inc. (BSR) is a brokerage firm that specializes in investment portfolios designed to…
A: Note: - As we can answer only up to three subparts we will answer the first three subparts(a, b, and…
Q: Two companies are producing widgets. It costs the first company q12 dollars to produce q1 widgets…
A: Given: First company Second company q12 dollars 0.5q22 dollars
Q: Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged…
A: The detailed solution is given in Steps ahead.
Q: There are three factories on a river, each of which emits two types of pollutants, labeled P1 and…
A: Cost to Process a ton of Factory Waste 1: $1500Reduces P1 by 0.10, P2 by 0.45 Cost to Process a ton…
Q: An investment of $300,000 is expected to generate the following cash inflows in six years: Year 1:…
A: Find the Given Details below: Given Details: Total Investment 300000 $ Cash Inflows Year 1…
Q: The owner of a snack food business wants to create two nut mixes for the holiday season. The regular…
A: Decision variable: Suppose-R be the no. of regular nut mixD be the no. of delux nut mix
Q: A firm is planning to spend $75,000 on advertising. It costs $3000 per minute to advertise on…
A:
Q: A firm offers three different prices on Its products, depending upon the quantity purchased. Since…
A: Objective Functions and Constraints: Based on the given details, we found the…
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: A firm offers three different prices on its products, depending upon the quantity purchased. Since…
A: Objective Functions and Constraints: Based on the given details, we found the…
Q: An investment advisor at RMC Financial Services wants to develop a model that can be used to…
A: x1 ,x2,x3 and x4 are corresponding ratio of stocks ,bonds, mutual funds and cash- x1+x2+x3+x4 = 1 x1…
Q: The cost of producing a certain commodity consists of P45.00 per unit for labor and material cost…
A: Formula to be used; Break even quantity = Fixed cost / Contribution margin
Q: FORUM Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf…
A: B = Number of Big shelves M = Number of Medium shelves Objective function: Maximize Z = 360B + 250M…
Q: The purchased and installation costs of some pieces of equipment are given as a function of weight…
A:
Q: A trail mix company has 200 pounds of peanuts and 150 pounds of raisins. A batch of house mix takes…
A: Given Information:
Q: A company makes two types of sofas, regular and long, at two locations, one in Msamvu and one in…
A: Below is the solution:-
Q: ayue Is The company is evaluating three different expansion plans: Minor, moderate, or major. They…
A:
Q: A company is considering two insurance plans with the following types of coverage and premiums: Plan…
A: Linear programming toll is the which takes into consideration certain linear relationships to obtain…
Q: a chain saw requires 4 hours of assembly and wood chipper 3 hours.A maximum of 36 hours of assembly…
A: Given Information:
Q: A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a…
A: Disclaimer: Since you have asked multiple question, so we will solve the first question for you. If…
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) = ?
A company manufactures two products. If it charges price pi for product i, it can sell qi units of product i,where q1 = 60−3p1 +p2 and q2 = 80−2p2 +p1. It costs $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of each product should the company produce, and what prices should it charge, to maximize its profit?
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 3 images
- 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%.Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?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.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.
- A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is 50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in England as a function of price (in pounds) is of the power type, with constant 27556759 and exponent 2.4. a. Develop a model for the companys profit (in dollars) as a function of the price it charges (in pounds). Then use a data table to find the profit-maximizing price to the nearest pound. b. If the exchange rate varies from its current value, does the profit-maximizing price increase or decrease? Does the maximum profit increase or decrease?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.)