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Question: the manager of a food processing plant that specializes in...

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The manager of a food processing plant that specializes in potato chips has developed an LP model to reflect processing times.

x1 = boxes of regular chips

x2 = boxes of crinkle cut chips

Maximize Z = .40x1 + .30x2 (profit)

subject to

Cutting 3.6x1 + .8x2 ≤ 144 minutes

Frying 3.2x1 + 1.6x2 ≤ 160 minutes

Packing 4.8x1 + 7.2x2 ≤ 576 seconds

Crinkle x2 ≤ 80 boxes

Crinkle x2 ≥ 20 boxes

x1, x2 ≥ 0

Briefly explain or define each of these parts of the model:

a. The .40 in the objective function.

b. The product of the .3 and x2 in the objective function.

c. The 144 minutes in the cutting constraint.

d. The 4.8 in the packing constraint.

e. x2 ≥ 20.

f. The product of 3.2 and x1 in the frying constraint.

g. What two key questions can be answered using this model?

The optimal solution is to produce 15 boxes of x1 and 70 boxes of x2 for a total maximal profit of $27.00. Determine each of the following:

h. The amount of each resource that will be used.

i. The amount of slack for each resource.

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