A manufacturer of skis produces two types: downhill and cross-country. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the maximum time available for manufacturing was increased to 135 hours? Manufacturing time per ski Finishing time per ski Profit per ski Downhill Cross-country Maximum Time Available 3 hours 2.5 hours 123 hours 1 hour £70 1.5 hours £70 57 hours
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- 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%.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 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…
- PMC Company manufactures and sells three lines of product with contribution margins per unit as follows: Product A = P12; Product B = P2; Product C = P5.Each unit of product requires production time as follows: Product A = 3 hours; Product B = 10 minutes; Product C = 2 hours.The company has plant capacity of 20,000 machine hours a month. The market can absorb 2,000 units of Product A, 24,000 units of Product B and 15,000 units of Product C. What is the most profitable product line on the basis of contribution margin per machine hour? A. ProductA B. ProductB C. ProductC 2. Compute the maximum contribution margin for the month that will meet the conditions statedA trail mix company has 200 pounds of peanuts and 150 pounds of raisins. A batch of house mix takes 20 pounds of peanuts and 10 pounds of raisins. A batch of fancy mix takes 10 pounds of peanuts and 15 pounds of raisins. Profit from a batch of house mix is $50 and from a batch of fancy mix is $60. How much of each type should be made to maximize profits? What is the maximum profit?Based on Brams and Taylor (2000). Suppose that EliLilly and Pfizer are going to merge. Merger negotiations must settle the following issues: ■ What will the name of the merged corporation be?■ Will corporate headquarters be in Indianapolis(Lilly wants this) or New York (Pfizer wants this)?■ Which company’s chairperson will be chairperson of the merged corporation?■ Which company gets to choose the CEO?■ On the issue of layoffs, what percentage of each company’s view will prevail?Brams developed a remarkably simple method for the two adversaries to settle their differences. (This same method could be used to settle differences between other adversaries, such as a husband and wife in a divorce, Arab and Israel in Middle East, and so on.) Each adversary allocates 100 points between all of the issues. These allocations are listed in the file P04_84.xlsx. For example, Lilly believes headquarters is worth 30 points, whereas Pfizer thinks headquarters is worth only 15 points. Layoffs may be…
- Creative Sports Design (CSD) manufactures a standard-size racket and an oversize racket. The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy. Each standard-size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two-week production period only 80 kilograms of the alloy are available. Each standard-size racket uses 10 minutes of manufacturing time and each oversize racket uses 12 minutes. Also, 40 hours of manufacturing timeare available each week. The profit contributions are $10 for each standard-size racket and $15 for each oversize racket. How many rackets of each type should CSD manufacture over the next two weeks to maximize the total profit contribution? a. Define decision variables and formulate the problem.b. Solve the problem using the graphical method.The cost data for Evencoat Paint for the year 2019 is as follows: Month Gallons ofPaintProduced EquipmentMaintenanceExpenses January 110,000 $70,700 February 68,000 66,800 March 71,000 67,000 April 77,000 68,100 May 95,000 69,200 June 101,000 70,300 July 125,000 70,400 August 95,000 68,900 September 95,000 69,500 October 89,000 68,600 November 128,000 72,800 December 122,000 71,450 A. Using the high-low method, express the company’s maintenance costs as an equation where x represents the gallons of paint produced. Then estimate the fixed and variable costs. Fixed cost $ Variable cost $Shoemakers of America forecasts the following demandfor each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000 pairs; month 6—5,000 pairs. Ittakes a shoemaker 15 minutes to produce a pair of shoes.Each shoemaker works 150 hours per month plus up to 40hours per month of overtime. A shoemaker is paid a regularsalary of $2,000 per month plus $50 per hour for overtime.At the beginning of each month, Shoemakers can either hireor fire workers. It costs the company $1,500 to hire a workerand $1,900 to fire a worker. The monthly holding cost perpair of shoes is 3% of the cost of producing a pair of shoeswith regular-time labor. (The raw materials in a pair of shoescost $10.) Formulate an LP that minimizes the cost ofmeeting (on time) the demands of the next six months. Atthe beginning of month 1, Shoemakers has 13 workers
- Shoemakers of America forecasts the following demandfor each of the next six months: month 1—5,000 pairs;month 2—6,000 pairs; month 3—5,000 pairs; month 4—9,000 pairs; month 5—6,000 pairs; month 6—5,000 pairs. Ittakes a shoemaker 15 minutes to produce a pair of shoes.Each shoemaker works 150 hours per month plus up to 40hours per month of overtime. A shoemaker is paid a regularsalary of $2,000 per month plus $50 per hour for overtime.At the beginning of each month, Shoemakers can either hireor fire workers. It costs the company $1,500 to hire a workerand $1,900 to fire a worker. The monthly holding cost perpair of shoes is 3% of the cost of producing a pair of shoeswith regular-time labor. (The raw materials in a pair of shoescost $10.) Formulate an LP that minimizes the cost of At the conclusion of the season, this method has beenused to determine ratings for college football and collegebasketball. What problems could be foreseen if this methodwere used to rate teams early in the…The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…25. Consider the following list of retail items sold in a small neighborhood gift shop.Average ProfitItem Annual Volume per ItemGreeting cards 3,870 $ 0.40T-shirts 1,550 1.25Men’s jewelry 875 4.50Novelty gifts 2,050 12.25Children’s clothes 575 6.85Chocolate cookies 7,000 0.10Earrings 1,285 3.50Other costume jewelry 1,900 15.00a. Rank the item categories in decreasing order of the annual profit. Classify eachin one of the categories as A, B, or C.b. For what reason might the store proprietor choose to sell the chocolate cookieseven though they might be her least profitable item?