XYZ Foods Inc. has a contract to produce 3000 pounds of trail mix for a conventi

Question

XYZ Foods Inc. has a contract to produce 3000 pounds of trail mix for a convention.   Ingredients available and cost per pound are peanuts ($2.50), raisons ($2.25), dried bananas ($1.50), dried cranberries ($3), and pretzel sticks ($1). There are 1000 pounds of peanuts available, 1400 pounds of pretzel sticks, 460 pounds of raisons, 400 pounds of bananas, and 500 pounds of cranberries.

The mix should contain at least 25% peanuts and at most 50% pretzel sticks. Bananas must be at least 10% the mix and raisons + cranberries must be at least 15% of the mix.

The company wants to minimize the cost of producing the 3000 pounds of trail mix. The company also wants to be able to easily modify the model – such as to increase the 3000 pounds to 3200 pounds without having to modify a bunch of constraints. (so for example, for the maximum 50% pretzel sticks, do not just use X5<=1500 – write the constraint in terms of the other variables)

Create the required Linear Programming model

Explanation / Answer

p - peanuts
q - raisons
r - dried bananas
s - dried cranberries
t - pretzel sticks

Minimize Cost = 2.5p + 2.25q + 1.5r + 3s + t
p <= 1000
t <= 1400
q <= 460
r <= 400
s <= 500

p >= 0.25*(p + q + r + s + t)
t <= 0.5 * (p + q + r + s + t)
r >= 0.1*(p + q + r + s + t)
q + s >= 0.15*(p + q + r + s + t)

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