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Question: the new manager of a food processing plant hopes to...

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The new manager of a food processing plant hopes to reduce costs by using linear programming to determine the optimal amounts in kilograms of two ingredients it uses,

x1 and x2. The manager has constructed this model:

Minimize Z = .40x1 + .40x2

Subject to

Protein 3x1 + 5x2 ≥ 30 grams

Carbohydrates 6x1 + 4x2 ≥ 48 grams

x1, x2 ≥ 0

a. Graph the constraints and identify the feasible region.

b. Determine the optimal solution and the minimum cost (Show your work).

c. There is a single optimal solution to part b above. However, if the objective function had been parallel to one of the constraints, there would have been two equally optimal solutions. If the cost of x2 remains at $.40, what cost of x1 would cause the objective function to be parallel to the carbohydrate constraint? Explain how you determined this.

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