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) 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 = 50x + 60y Subject to

2x + y 16

x + y 10

x 0,y 0

P =