04 Jun Question A Nut Case The Molokai Nut Company (MNC) makes four different products from macadamianuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolatec
Question
A Nut Case
The Molokai Nut Company (MNC) makes four different products from macadamianuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolatecoatednut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain
CASE 4.1
roasted nuts (Roasted). The company is barely able to keep up with the increasingdemand for these products. However, increasing raw material prices and foreign competitionare forcing MNC to watch its margins to ensure it is operating in the mostefficient manner possible. To meet marketing demands for the coming week, MNCneeds to produce at least 1,000 pounds of the Whole product, between 400 and500 pounds of the Cluster product, no more than 150 pounds of the Crunch product,and no more than 200 pounds of Roasted product.Each pound of the Whole, Cluster, Crunch, and Roasted product contains, respectively,60%, 40%, 20%, and 100% macadamia nuts with the remaining weight made upof chocolate coating. The company has 1100 pounds of nuts and 800 pounds of chocolateavailable for use in the next week. The various products are made using four differentmachines that hull the nuts, roast the nuts, coat the nuts in chocolate (ifneeded), and package the products. The following table summarizes the time requiredby each product on each machine. Each machine has 60 hours of time available in thecoming week.
Minutes Required per PoundMachine Whole Cluster Crunch Roasted
Hulling 1.00 1.00 1.00 1.00Roasting 2.00 1.50 1.00 1.75Coating 1.00 0.70 0.20 0.00Packaging 2.50 1.60 1.25 1.00The controller recently presented management with the following financial summary
of MNC’s average weekly operations over the past quarter. From this report, the controller
is arguing that the company should cease producing its Cluster and Crunchproducts.
ProductWhole Cluster Crunch Roasted Total
Sales Revenue $5,304 $1,800 $510 $925 $8,539Variable CostsDirect materials $1,331 $560 $144 $320 $2,355Direct labor $1,092 $400 $96 $130 $1,718Manufacturing overhead $333 $140 $36 $90 $599Selling & Administrative $540 $180 $62 $120 $902Allocated Fixed CostsManufacturing overhead $688 $331 $99 $132 $1,250Selling & Administrative $578 $278 $83 $111 $1,050Net Profit $742 -$88 -$11 $22 $665Units Sold 1040 500 150 200 1890Net Profit Per Unit $0.71 -$0.18 -$0.07 $0.11 $0.35
a. Do you agree with the controller’s recommendation? Why or why not?
b. Formulate an LP model for this problem.c. Create a spreadsheet model for this problem and solve it using Solver.d. What is the optimal solution?e. Create a sensitivity report for this solution and answer the following questions.f. Is the solution degenerate?g. Is the solution unique?h. If MNC wanted to decrease the production on any product, which one would yourecommend and why?
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