Answer the following questions on Linear Programming (use the class videos/notes to review the concepts).

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 $0.1 $0,15

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. Assume that the calcium requirement increases from 50 to 54 units. Calculate and provide an economic interpretation of the shadow price associated with calcium.(3)