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\fSolve 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 = 90 Subject to x+ y = 50 x + 2y s 90 x20, y 20Formulate 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 $66 for each goat and $99 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 $\f\f\f\fUse the region below to find the maximum value. (If such a value does not exist, enter DNE.) 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 (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 = 16 Subject to x+ y = 10 x20, y 20 PE