Please help with six problems below

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 = 20x + 12y 2x + y s 90 Subject to x+ y s 50 x + 2y $ 90 x20, y 20 PUse the region below to find the maximum value. (If such a value does not exist, enter ONE.) Maximum of P = 5x + 3y 30 (0, 20) (10, 20) (15, 15) (0, 10) (10,0) (15, 0) 30Use the region below to find the minimum value. (If such a value does not exist, enter DNE.) Minimum of C = 9x + 2y G (0, 60) 30 (20, 20) (100, 0) 30% (60, 0)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 = 60x + 70y 2x + y s 16 Subject to x+ y s 10 x20, y 20 P=Solve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then nding it if it does exist. (If an answer does not exist, enter DNE.) Minimize C = 5x + 25y 2x+5y22o Subject to {x 2 0' y 2 G