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 120 hours of cutting time and 120 hours of sewing time 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 through the firms mail order catalog 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, how many units of each model should it manufacture to maximize the total profit contribution?

Explanation / Answer

Given the below information about the Expedition Outfitters manufactures Mount Everest Parka Rocky Mountain Parkha Cutting Time 30 and 20 .Sewing Time 45 and 15 Labor and Material Cost $150 and $50 Retail Price $250 and $200

Let Number of units of each be x and y

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

Objective Function = Maximize (100x+150y)

Constraints: 1) 30*x+20*y <=120*60 2) 45*x+15*y<=120*60 3) x>=20%*(x+y) or x>=4y

We will use solver to solve the above linear programming.

So, Total Number of units 184.6154

Mount Everest Parka = 147.6923077

Rocky Mountain Parkha = 36.92307692

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