1 - Sketch the system of inequalities. x + 2y 32 x 0, y 0 2 - Sketch the system of inequalities. 3 - Sketch the system of inequalities. 4 - Sketch the system of inequalities. List all vertices and identify the region as "bounded" or "unbounded." 5 - Formulate the situation as a system of inequalities. (Let x represent the number of goats the farmer can raise and y represent the number of llamas.) A rancher raises goats and llamas on his 400-acre ranch. Each goat needs 2 acres of land and requires $90 of veterinary care per year, while each llama needs 5 acres of land and requires $72 of veterinary care per year. If the rancher can afford no more than $11,880 for veterinary care this year, how many of each animal can he raise? 6 - Use the region below to find the maximum value. (If such a value does not exist, enter DNE.) Maximum of P = 5x + 3y 7 - Use the region below to find the minimum value. (If such a value does not exist, enter DNE.) Minimum of C = 7x + y 8 - 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.) 9 - 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.) 10 - 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.) 11 - 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? 1 - Sketch the system of inequalities. x + 2y 32 x 0, y 0 The vertices are 0,0 , 32,0 , 0,16 . The region is bounded. 2 - Sketch the system of inequalities. The vertices are 0,0 , 32,0 , 0,16 . The region is bounded. 3 - Sketch the system of inequalities. The vertices are 0,0 , 8,1 , 9,0 , 0,5 . The region is bounded. 4 - Sketch the system of inequalities. List all vertices and identify the region as "bounded" or "unbounded." The vertices are 0,8 , 3, 4 . The region is unbounded. 5 - Formulate the situation as a system of inequalities. (Let x represent the number of goats the farmer can raise and y represent the number of llamas.) A rancher raises goats and llamas on his 400-acre ranch. Each goat needs 2 acres of land and requires $90 of veterinary care per year, while each llama needs 5 acres of land and requires $72 of veterinary care per year. If the rancher can afford no more than $11,880 for veterinary care this year, how many of each animal can he raise? Constraints land requirements 2 x 5 y 400 veterinary care 90 x 72 y 11880 1040 944 The vertices are 0,0 , , , 105.6,0 , 0,80 17 17 6 - Use the region below to find the maximum value. (If such a value does not exist, enter DNE.) Maximum of P = 5x + 3y maximum occur at (15,15) and value is P=120 7 - Use the region below to find the minimum value. (If such a value does not exist, enter DNE.) Minimum of C = 7x + y minimum occur at (0,60) and minimum value is C=60 8 - 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.) Maximum value occur at (0,10) and value is P=400 9 - 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.) minimum occur at (10,0) and minimum value is C=150 10 - 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.) Maximum occur at (40,10) and maximum value is P=690 11 - 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? Let x denotes the number of goat and y the number of llamas. Constraints land requirements 2 x 5 y 400 veterinary care 100 x 80 y 13200 Objective function is maximize P 48 x 72 y The rancher should raise 100 goats and 40 llamas for a maximum profit of $7680