3) Solve the following LP

Maximize $4x + $5y

Subject to 4x + 5y 72

6x + 5y 27

-3x + 8y 0

x, y 0

a) Write the original optimal solution and objective function value.

b) What is the optimal solution and objective function value if the profit per unit of x decreases to $1?

c) What is the optimal solution and objective function value if the first constraint changes to 4x + 5y 80

d) What is the optimal solution and objective function value if the third constraint changes to -3x + 8y 0?

#4) Solve the following LP

Maximize $5x + $6y

Subject to 2x + 3y 10 (labor, in hours)

6x + 6y 36 (materials, in pounds)

7x + 5y 40 (storage, in square feet)

x, y 0

a) Write the original optimal solution and objective function value.

b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material?

c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?

d) What is the optimal solution and objective function value if you give up 1 hour of labor and get 1.5 pounds of material?

e) What is the optimal solution and objective function value if you introduce a new product that has a profit contribution of $2? Each unit of this product will use 1 hour of labor, 1 pound of material, and 2 square feet of storage space.

#5) Solve the following LP

	Oak Tables	Oak Chairs	Cherry Tables	Cherry Chairs	Pine Tables	Pine Chairs
Number of Units
Maximize Profit	75	35	90	60	45	20
Constraints:
Labor Hours	7.5	3.5	9.0	6.0	4.5	2.0		<=	1000
Oak (lbs.)	200	30						<=	2150
Cherry (lbs.)			240	36				<=	3800
Pine (lbs.)					180	27		<=	8500
Minimum Oak Tables	1							>=	3
Minimum Cherry Tables			1					>=	3
Minimum Oak Chairs		1						>=	10
Minimum Cherry Chairs				1				>=	10
Minimum Pine Chairs						1		>=	5
							LHS	SIGN	RHS

a) Write the original optimal solution and objective function value.

b) What is the optimal solution and objective function value if the profit for oak tables increases to $83?

c) What is the optimal solution and objective function value if the profit for pine chairs decreases to $13?

d) What is the optimal solution and objective function value if the profit for pine tables increases by $20?

e) What is the optimal solution and objective function value if the company is required to make at least 20 pine chairs?

f) What is the optimal solution and objective function value if the company is required to make no more than 55 cherry chairs?