6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) WebAssign Unit 4 Homework Assignment (4.1, 4.2) (Homework) Current Score : - / 36 armstrong Olivier MAT230, section MAT230.30 MOD5 2017, Summer 1 2017 Instructor: James Segala Due : Sunday, June 25 2017 11:59 PM EDT 1. -/5 pointsBerrFinMath1 4.1.001. Sketch the system of inequalities. x + 2y 28 x 0, y 0 List all vertices. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = Identify the region as "bounded" or "unbounded." bounded unbounded Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 1/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) 2. -/6 pointsBerrFinMath1 4.1.002. Sketch the system of inequalities. 2x + y 10 x 12 x 0, y 0 List all vertices. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = (x, y) = Identify the region as "bounded" or "unbounded." bounded unbounded https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 2/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 3/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) 3. -/6 pointsBerrFinMath1 4.1.003. Sketch the system of inequalities. x + 2y 10 x + y 9 x 0, y 0 List all vertices. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = (x, y) = Identify the region as "bounded" or "unbounded." bounded unbounded https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 4/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) Show My Work (Optional) 4. -/4 pointsBerrFinMath1 4.1.005. Sketch the system of inequalities. List all vertices and identify the region as "bounded" or "unbounded." 6x + 3y 24 y 2 x 0 List all vertices. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = Identify the region as "bounded" or "unbounded." bounded unbounded Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 5/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) 5. -/7 pointsBerrFinMath1 4.1.007. 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 800acre ranch. Each goat needs 4 acres of land and requires $70 of veterinary care per year, while each llama needs 10 acres of land and requires $56 of veterinary care per year. If the rancher can afford no more than $9,240 for veterinary care this year, how many of each animal can he raise? (land requirements) (veterinary care) x 0, y 0 Sketch the feasible region. Find the vertices. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 6/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) (x, y) = Show My Work (Optional) 6. -/1 pointsBerrFinMath1 4.2.001. Use the region below to find the maximum value. (If such a value does not exist, enter DNE.) Maximum of P = 4x + 3y P = Show My Work (Optional) 7. -/1 pointsBerrFinMath1 4.2.003. Use the region below to find the minimum value. (If such a value does not exist, enter DNE.) Minimum of C = 7x + 2y C = Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 7/8 6/16/2017 Unit 4 Homework Assignment (4.1, 4.2) 8. -/1 pointsBerrFinMath1 4.2.005. 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 + 80y 2x + y 16 Subject to x + y 10 x 0, y 0 P = Show My Work (Optional) 9. -/1 pointsBerrFinMath1 4.2.006. 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.) Minimize C = 15x + 75y Subject to 2x + 5y 20 x 0, y 0 C = Show My Work (Optional) 10.-/1 pointsBerrFinMath1 4.2.008. 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 2x + y 90 x + y 50 Subject to x + 2y 90 x 0, y 0 P = Show My Work (Optional) 11.-/3 pointsBerrFinMath1 4.2.009. 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 400acre 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 $ . Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106774 8/8 1. Vertices: (0,0) (28,0) (0,14) The region is bounded. 2. The vertices are: (0, 0) (12, 0) (0, 10) (12, 34) The region is bounded. 3. The vertices are: (0,0) (8,0) (8,1) (0,5) The region is bounded. 4. The vertices are: (0, 8) (3, 2) The region is unbounded. 5. 4x + 10y 70x + 56y 800 9240 Feasible region The vertices are: (0, 0) (132, 0) (100, 40) (0, 80)