1) Solve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then finding it if it does exist. (If an answer does not exist, enter DNE.)

MinimizeC = 15x + 45y

Subject to

2x + 5y 20

x 0,

y 0

C =

2) Solve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then finding it if it does exist. (If an answer does not exist, enter DNE.)

Maximize

P = 15x + 9y

Subject to:

2x + y 90

x + y 50

x + 2y 90

x 0,y 0

P =

3) Formulate the situation as a linear programming problem by identifying the variables, the objective function, and the constraints. Be sure to state clearly the meaning of each variable. Determine whether a solution exists, and if it does, find it. State your final answer in terms of the original question.

A rancher raises goats and llamas on his 400-acre ranch. Each goat needs 2 acres of land and requires $100 of veterinary care per year, and each llama needs 5 acres of land and requires $80 of veterinary care per year. The rancher can afford no more than $13,200 for veterinary care this year. If the expected profit is $48 for each goat and $72 for each llama, how many of each animal should he raise to obtain the greatest possible profit?

The rancher should raise [ ] goats and [ ] llamas for a maximum profit of $ [ ]