Expedition outfitters manufactures a variety of specially clothing for hiking, s

Question

Expedition outfitters manufactures a variety of specially clothing for hiking, skiing and mountain climbing. The company has decided to begin production on two new parkas designed for use in extremely cold weather: The Mount Everest Parka and the Rocky Mountain Parka. Expedition's manufacturing plant has 200 hours of cutting time (i.e., 2,000 minutes) and 250 hours of sewing time (i 15,000 minutes) available for producing these two parkas. Each Mount Everest Parka requires 30 minutes of cutting time and 45 minutes of sewing time, and each Rocky Mountain Parka requires 20 minutes of cutting time and 15 minutes of sewing time. The labor and material cost is $150 for each Mount Everest Parka and $50 for each Rocky Mountain Parka, and the retail prices are $250 for the Mount Everest Parka and $200 for the Rocky Mountain Parka. Because management believes that Mount Everest Parka will enhance the image of the firm, at least 20% of the total production must consist of this model. Assuming that Expedition can sell as many coats of each type as it can produce, formulate a linear program to determine how many units of each model to make to optimize the total profit. [Note: Profit revenue (sales)- cost Let number of Mount Everest Parkas to make Lety number of Rocky Mountain Parkas to make [Choose the best equation to match each of the following description. Note: The sign s shown as and the sign is shown as in the equations.] Objective function Choose Constraint for cutting time (minutes) I Choose Constraint for sewing time (minutes) Choose

Explanation / Answer

Let x number of Mount Everest Parka and y number of Rocky Mountain Parka be produced

Total Cutting Time=30x+20y<=12000

Total Sewing Time=45x+15y<=15000

Total Profit=250x+200y-(150x+50y)=100x+150y

Total Production=x+y

And x>=0.2(x+y) gives 4x>=y

Hence after solving for maximum profit against x,y we get

x=109,y=436

Profit=73600

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