a. What is the optimal production plan and associated cost?

b. Is the solution degenerate?

c. Is the solution unique?

d. What would happen to the total cost if one of the Dobbie machines broke and could not be used at all during the quarter?

e. What would happen to the total cost if an additional Dobbie machine was purchased and available for the quarter?

f. What would happen to the total cost if one of the Pantera machines broke and could not be used at all during the quarter?

g. What would happen to the total cost if an additional Pantera machine was purchased and available for the quarter?

h. Explain the shadow prices and the values in the “Allowable Increase” column of the Sensitivity Report for the products that are being outsourced.

i. How much money does it cost to produce carpet order 2? How much would the total cost decrease if that order were eliminated? Explain.

j. If the carpets in orders 5 through 15 all sell for the same amount, which type of carpet should Kamm encourage its sales force to sell more of? Why?

k. If the cost of buying the carpet in order 1 increased to $2.80 per yard, would the optimal solution change? Why?

l. If the cost of buying the carpet in order 15 decreased to $1.65 per yard, would the optimal solution change? Why?

If your home or office is carpeted, there’s a good chance that carpet came from Dalton, Georgia—also known as the “Carpet Capital of the World.” Manufacturers in the Dalton area produce more than 70 percent of the total output of the $9 billion world-wide carpet industry. Competition in this industry is intense, which forces producers to strive for maximum efficiency and economies of scale. It also forces producers to continually evaluate investments in new technology.

Kamm Industries is one of the leading carpet producers in the Dalton area. Its owner, Geoff Kamm, has asked for your assistance in planning the production schedule for the next quarter (13 weeks). The company has orders for 15 different types of carpets that the company can produce on either of two types of looms: Dobbie looms and Pantera looms. Pantera looms produce standard tufted carpeting. Dobbie looms also can produce standard tufted carpeting, but they also allow the incorporation of designs (such as flowers or corporate logos) into the carpeting. The following table summarizes the orders for each type of carpet that must be produced in the coming quarter along with their production rates and costs on each type of loom, and the cost of subcontracting each order. Note that the first 4 orders involve special production requirements that can be achieved only on a Dobbie loom or via subcontracting. Assume that any portion of an order may be subcontracted.

Kamm currently owns and operates 15 Dobbie looms and 80 Pantera looms. To maximize efficiency and keep pace with demand, the company operates 24 hours a day, 7 days a week. Each machine is down for routine maintenance for approximately 2 hours per week. Create a spreadsheet model for this problem that can be used to determine the optimal production plan.

Transcribed Image Text:

6669 664 53455534454 66 5 6 6 6 6 6 8 50 44 64 57 271 5553445 ( -4, 4 4 4 5 3 4 5 1 123456789012345