The problem below involves three variables. Solve it with the simplex method, Excel, or some other technology. A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 13 lots, 52,400 labor-hours, and $3,684,200 available for the contractor's use. Aries Belfair Wexford Labor-hours 3,000 3,700 5,000 Capital $205,000 $279,600 $350,000 Profit $20,000 $25,000 $30,000 (a) Building how many of each type of house will maximize his profit? Aries houses Belfair houses Wexford houses (b) What is the maximum possible profit? $

The problem below involves three variables. Solve it with the simplex method, Excel, or some other technology. A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 13 lots, 52,400 labor-hours, and $3,684,200 available for the contractor's use. Aries Belfair Wexford Labor-hours 3,000 3,700 5,000 Capital $205,000 $279,600 $350,000 Profit $20,000 $25,000 $30,000 (a) Building how many of each type of house will maximize his profit? Aries houses Belfair houses Wexford houses (b) What is the maximum possible profit? $

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.4: Marketing Models

Problem 30P: Seas Beginning sells clothing by mail order. An important question is when to strike a customer from...

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	Aries	Belfair	Wexford
Labor-hours	3,000	3,700	5,000
Capital	$205,000	$279,600	$350,000
Profit	$20,000	$25,000	$30,000

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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?
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 44 32 Hours required to complete all the cherry cabinets 61 46 34 Hours available 35 25 30 Cost per hour $36 $43 $56 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final…
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 47 40 27 Hours required to complete all the cherry cabinets 64 51 36 Hours available 40 30 35 Cost per hour $34 $41 $52 For example, Cabinetmaker 1 estimates it will take 47 hours to complete all the oak cabinets and 64 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final…
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c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? If required, round your answers to three decimal places. If your answer is zero, enter "0". Explain. ✓ because Cabinetmaker 1 has dual value Yes ✓ of No -1.84 ✔ ✓ of Therefore, each additional hour of time for cabinetmaker 1 will reduce total cost by $ d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? If required, round your answers to three decimal places. If your answer is zero, enter "0". Use a minus sign to indicate the negative figure. Explain. ✔ because Cabinetmaker 2 has a slack 1.84 ✔ per hour, up to a maximum of 30 X hours. Alternatively, the dual value is 50 ✓ hours. 0.00 ✓ which means that adding one hour to this constraint will decrease total cost by $ 0.00 ✓.
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Mark has a company that produces tables and chairs, both having two different models. The product models and related information are given in the following table. Wood costs 3000 $ per cubic meter and 200 m3 of wood are available for the upcoming month. The cost of labor is 40 $/hour and there are 6000 hours of labor available in a month. Mark sells his products to a big chain retail company. The company purchases all products whatever Mark produces. Mark formulates an LP as follows to determine the optimal monthly production plan such that he maximizes the total profit. Decision Variables: X1 : number of basic tables to be produced. X2 : number of elegant tables to be produced. X3 : number of basic chairs to be produced. X4 :number of elegant chairs to be produced. Max Z = 140 X1 + 345 X2 + 120 X3 + 260 X4 ( maximize total profit) Subject to 0.11 X1 + 0.13 X2 + 0.06 X3 + 0.07 X4 ≤ 200 (constraint on the available amount of wood) 2 X1 + 4.5 X2 + 1.5 X3 + 4 X4 ≤ 6000…
I need a detailed explanation and assistance to solve this proble: A client asks his stockbroker to invest $100,000 for maximum annual income, subject to the three conditions: Spread the investment over no more than three different stocks. Put no more than 40 percent of the money into any one stock Put a minimum of $10,000 into an oil stock. The broker has identified three stocks for investment. Their estimated annual returns per share and price per share are shown in the following table: Stock Price per Share Estimate Annual Return per Share Oil $120 $11 Auto $52 $4 Pharmaceutical $18 $2 The client wishes to use LP to determine the optimal number of shares to buy for each stock, so as to maximize the total estimated return. a) Write down the decision variables. b) Write down the optimization statement for the objective function. c) Write down the constraints.
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Jerry Wei, the hospital administrator at St. Charles General, must appoint head nurses to four newly established departments: urology, cardiology, orthopedics, and obstetrics. In anticipation of this staffing problem, he had hired four nurses, considered their backgrounds, personalities, and talents, and developed a cost scale ranging from 0 to 100 to be used in the assignment. A 0 for a nurse being assigned to the cardiology unit implies that the nurse would be perfectly suited to that task. A value close to 100, on the other hand, would imply that he or she is not at all suited to head that unit. The accompanying table gives the complete set of cost figures that the hospital administrator feels represented all possible assignments. Which nurse should be assigned to which unit? Department Urology Cardiology Orthopedics 28 18 15 32 48 23 51 36 24 25 38 55 Determine the assignment of nurses. The total cost is (enter your response as a whole number). Nurse Kitty Forman Carol Hathaway…
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