An appliance company is thinking of manufacturing and selling trash compactors. The manufacturing costs and selling...

  

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An appliance company is thinking of manufacturing and selling trash compactors. The manufacturing costs and selling prices are projected to vary over the next 6 months as follows: Month July August September October November December Manufacturing Cost $60 $60 $50 $60 $70 Selling Price $80 $60 $70 $80 $90 It cannot sell any compactors in July, and it does not manufacture any compactors in December. All compactors manufactured during any month are shipped out (i.e., sell or store) in one large load at the end of that month. The firm can manufacture as many as 250 units and sell as many as 300 units per month, but its operation is also limited by the size of its warehouse, which holds a maximum of 100 compactors (in total). The firm has no compactors on hand (inventory) at the beginning of July and wishes to have no compactors on hand (inventory) at the end of December. Determine the number of compactors to manufacture and sell each month, in order to maximize the firm's profit. And what is the the maximum profit? Problem 2: (50 pts) Consider the following weekly resource allocation problem faced by the production manager of XYZ Company. XYZ sells three types of computer; the PC (type X), the notebook computer (type Y), and the workstation (type Z). The net profit from each is: Type X: $350; Type Y: $470; and Type Z: $610, where net profit equals the sales price of each computer minus the direct costs of purchasing components, producing computer cases, and assembling and testing the computer. Assume that all production during any given week can and will be sold immediately. For a particular week, 120 hours are available on the Type A test equipment, where X and Y's are tested, and 48 hours are available on the Type B test equipment, where Z's are tested. The testing of each computer takes one hour, regardless of type. Production is constrained by the availability of 2000 labor hours for product assembly. Each Type X takes 10 labor hours, type Y takes 15 labor hours and type Z takes 20 labor hours. Other activities have virtually unlimited resources. (i) Construct an LP model of this problem. (ii) Use the SOLVER in Excel to solve this problem. Interpret your output and answer the following questions. Please submit your supporting Excel spreadsheet. a) How many PCs, Notebook computers, and workstations should be produced? b) What is the optimal total profit? c) If you were given additional funding, where would you invest that money to increase your profit and why? (Hint: testing equipment? If so, which ones A, B or both? production labor? Both testing equipment and production labor? make sure to articulate the reason(s) for your investment decision, such as using sensitivity analysis.) An appliance company is thinking of manufacturing and selling trash compactors. The manufacturing costs and selling prices are projected to vary over the next 6 months as follows: Month July August September October November December Manufacturing Cost $60 $60 $50 $60 $70 Selling Price $80 $60 $70 $80 $90 It cannot sell any compactors in July, and it does not manufacture any compactors in December. All compactors manufactured during any month are shipped out (i.e., sell or store) in one large load at the end of that month. The firm can manufacture as many as 250 units and sell as many as 300 units per month, but its operation is also limited by the size of its warehouse, which holds a maximum of 100 compactors (in total). The firm has no compactors on hand (inventory) at the beginning of July and wishes to have no compactors on hand (inventory) at the end of December. Determine the number of compactors to manufacture and sell each month, in order to maximize the firm's profit. And what is the the maximum profit? Problem 2: (50 pts) Consider the following weekly resource allocation problem faced by the production manager of XYZ Company. XYZ sells three types of computer; the PC (type X), the notebook computer (type Y), and the workstation (type Z). The net profit from each is: Type X: $350; Type Y: $470; and Type Z: $610, where net profit equals the sales price of each computer minus the direct costs of purchasing components, producing computer cases, and assembling and testing the computer. Assume that all production during any given week can and will be sold immediately. For a particular week, 120 hours are available on the Type A test equipment, where X and Y's are tested, and 48 hours are available on the Type B test equipment, where Z's are tested. The testing of each computer takes one hour, regardless of type. Production is constrained by the availability of 2000 labor hours for product assembly. Each Type X takes 10 labor hours, type Y takes 15 labor hours and type Z takes 20 labor hours. Other activities have virtually unlimited resources. (i) Construct an LP model of this problem. (ii) Use the SOLVER in Excel to solve this problem. Interpret your output and answer the following questions. Please submit your supporting Excel spreadsheet. a) How many PCs, Notebook computers, and workstations should be produced? b) What is the optimal total profit? c) If you were given additional funding, where would you invest that money to increase your profit and why? (Hint: testing equipment? If so, which ones A, B or both? production labor? Both testing equipment and production labor? make sure to articulate the reason(s) for your investment decision, such as using sensitivity analysis.)

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