Please use the attached file.

1. /5 pointsBerrFinMath1 4.1.001. Sketch the system of inequalities.

x + 2y 36 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

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7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

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7/23/2016

Unit 4 Homework Assignment (4.1, 4.2)

2. /6 pointsBerrFinMath1 4.1.002. Sketch the system of inequalities.

2x + y 6 x8 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) =

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7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

(x, y) =

Identify the region as "bounded" or "unbounded." bounded

unbounded

Show My Work (Optional)

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7/23/2016

Unit 4 Homework Assignment (4.1, 4.2)

3. /6 pointsBerrFinMath1 4.1.003. Sketch the system of inequalities.

x + 2y 6 x+y5 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) =

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7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

(x, y) =

Identify the region as "bounded" or "unbounded." bounded

unbounded

Show My Work (Optional)

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7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

4. /4 pointsBerrFinMath1 4.1.005. Sketch the system of inequalities. List all vertices and identify the region as "bounded" or "unbounded."

4x + 3y 24 y4 x0

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)

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7/23/2016 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 400acre 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?

(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) =

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7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

(x, y) =

(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.)

Maximumof P=5x+2y P=

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7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

7. /1 pointsBerrFinMath1 4.2.003. Use the region below to find the minimum value. (If such a value does not exist, enter DNE.)

Minimumof C=9x+3y C=

Show My Work (Optional)

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 = 30x + 80y

2x + y 16 Subject to x + y 10

x0, y0

P=

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 = 5x + 15y

Show My Work (Optional)

Subject to C=

2x + 5y 20 x0, y0

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11/12

7/23/2016 Unit 4 Homework Assignment (4.1, 4.2)

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

Subject to P=

P = 15x + 9y

2x + y 90 x + y 50 x + 2y 90 x0, y0

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 $60 for each goat and $90 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)

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12/12

7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) WebAssign Unit 4 Homework Assignment (4.1, 4.2) (Homework) Current Score : - / 36 Ryan Manuel MAT230, section MAT230.31 MOD6 2016, Summer 2 2016 Instructor: Kathleen Ferguson Due : Sunday, August 21 2016 11:59 PM EDT https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 1/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) 1. -/5 pointsBerrFinMath1 4.1.001. Sketch the system of inequalities. x + 2y 36 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 https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 2/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 3/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) 2. -/6 pointsBerrFinMath1 4.1.002. Sketch the system of inequalities. 2x + y 6 x 8 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) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 4/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) (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=13960001 5/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) 3. -/6 pointsBerrFinMath1 4.1.003. Sketch the system of inequalities. x + 2y 6 x + y 5 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) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 6/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) (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=13960001 7/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) 4. -/4 pointsBerrFinMath1 4.1.005. Sketch the system of inequalities. List all vertices and identify the region as "bounded" or "unbounded." 4x + 3y 24 y 4 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=13960001 8/12 7/23/2016 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 400acre 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? (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) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 9/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) (x, y) = (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 = 5x + 2y P = Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 10/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) 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 = 9x + 3y C = Show My Work (Optional) 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 = 30x + 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 = 5x + 15y Subject to 2x + 5y 20 x 0, y 0 C = Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=13960001 11/12 7/23/2016 Unit 4 Homework Assignment (4.1, 4.2) 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 $60 for each goat and $90 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=13960001 12/12 Sol: (1) x , y 0, 0 x , y 0, 18 x , y 36, 0 Bounded Sol: (2) x , y 0, 0 x , y 0, 6 x , y 8, 22 x , y 8, 0 Bounded Sol: (3) x , y 0, 0 x , y 0, 3 x , y 4, 1 x , y 5, 0 Bounded Sol: (4) x , y 0, 8 x , y 3, 4 Unbounded Sol: (5) x , y 0, 0 x , y 0, 80 x , y 100, 40 x , y 132, 0 Bounded Sol: (6) Sol: (7) P 5 15 2 15 105 C 9 0 3 60 180 land requirement 200, 200 veteriary care 9000, 2880 Sol: (8) x , y 0, 0 x , y 8, 0 x , y 6, 4 x , y 0, 10 Bounded Sol: (9) P 30 0 80 10 800 x , y 0, 4 x , y 10, 0 Unbounded Sol: (10) P 5 10 15 0 50 x , y 0, 0 x , y 45, 0 x , y 40, 10 x , y 10, 40 x , y 0, 45 P 15 40 9 10 690 Bounded Sol: (11) x = number of goats y = number of llamas x y limit acres of land 2 5 400 cost of vet care 100 80 13,200 profit 60 90 Objective function: P = 60x + 90y (maximize) Constraints: 2x + 5y x 0 y Corner points: (0, 80) 400 100x + 80 y 13,200 0 (100, 40) (132, 0) P (0, 80) = 60(0) + 90 (80) = $7,200 P (100, 40) = 60(100) + 90 (40) = $9,600 (max) P (132, 0) = 60(132) + 90 (0) = $7,920 The rancher should raise 100 goats and 40 llamas to earn a maximum profit of $9,600. Sol: (1) x , y 0, 0 x , y 0, 18 x , y 36, 0 Bounded Sol: (2) x , y 0, 0 x , y 0, 6 x , y 8, 22 x , y 8, 0 Bounded Sol: (3) x , y 0, 0 x , y 0, 3 x , y 4, 1 x , y 5, 0 Bounded Sol: (4) x , y 0, 8 x , y 3, 4 Unbounded Sol: (5) x , y 0, 0 x , y 0, 80 x , y 100, 40 x , y 132, 0 Bounded Sol: (6) Sol: (7) P 5 15 2 15 105 C 9 0 3 60 180 land requirement 200, 200 veteriary care 9000, 2880 Sol: (8) x , y 0, 0 x , y 8, 0 x , y 6, 4 x , y 0, 10 Bounded Sol: (9) P 30 0 80 10 800 x , y 0, 4 x , y 10, 0 Unbounded Sol: (10) P 5 10 15 0 50 x , y 0, 0 x , y 45, 0 x , y 40, 10 x , y 10, 40 x , y 0, 45 P 15 40 9 10 690 Bounded Sol: (11) x = number of goats y = number of llamas x y limit acres of land 2 5 400 cost of vet care 100 80 13,200 profit 60 90 Objective function: P = 60x + 90y (maximize) Constraints: 2x + 5y x 0 y Corner points: (0, 80) 400 100x + 80 y 13,200 0 (100, 40) (132, 0) P (0, 80) = 60(0) + 90 (80) = $7,200 P (100, 40) = 60(100) + 90 (40) = $9,600 (max) P (132, 0) = 60(132) + 90 (0) = $7,920 The rancher should raise 100 goats and 40 llamas to earn a maximum profit of $9,600