A manager has formulated the following LP problem.

HW
(15 points)

Answer the following questions on Linear
Programming (use the class notes to review the concepts). Both questions are
graded (G).
1. A manager has formulated the following LP
problem. Draw the graph and find the optimal solution. (In each, all variables
are nonnegative). (3)
Maximize:
10x+15y, subject to 2x+5y ≤ 40 and 6x+3y ≤ 48.
2.
An athlete carefully watches her intake of calcium, protein, and calories.
Her
breakfast diet consists mainly of milk and cereal, whose prices and
nutrient
contents appear in the following table:
Milk
(1 oz.) Cereal (1 oz.)
Calcium 2 2
Protein 2 6
Calories 6 2
Price $.10 $.15
She
seeks a diet that supplies at least 50 units of calcium, 90 units of
protein,
and 66 calories at minimum cost.

a.
Formulate, graph, and solve this decision problem. What is the
minimum cost of meeting the nutrient
requirements? (9)

b.
Calculate and provide an economic interpretation of the shadow
price associated with calcium. (3)

 

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