Fashion Designs produces four clothing products pants, dresses, skirts and blouses. The company needs to make at least 300 garments in total. Further, the number of blouses produced should be more than the number of skirts by at least 20. The firm has 800 hours of cutting time, 720 hours of sewing time and 600 hours of packing and inspecting time. Each pant requires 1 hour of cutting time, 4 hours of sewing time and 2 hours of packing and inspecting time. Each dress requires 1 hour of cutting time, 2 hours of sewing time and 2 hours of packing and inspecting time. Each skirt requires 4 hours of cutting time, 1 hour of sewing time and 1 hour of packing and inspecting time. Each blouse requires 1 hour of cutting time, 3 hours of sewing time and 1 hour of packing and inspecting time. The profit from a pant, dress, skirt and blouse are respectively $15, $16, $12 and $16.

LP Formulation

Decision Variables

P - # of pants to produce

D - # of dresses to produce

S - # of skirts to produce

B - # of blouses to produce

Objective function

Maximize z = 15P + 16D + 12S + 16B

Constraints

Cutting: P + D + 4S + B < 800

Sewing: 4P + 2D + S + 3B < 720

Packing & Inspect: 2P + 2D + S + B < 600

Min. production: P + D + S + B > 300

Blouse & skirt: B > S + 20

P,D,S,B > 0

The sensitivity report for the problem is given below.

Each statement in the following questions refers to the original problem. In other words, each statement is independent of other statements. For each statement given you are asked to determine if the optimal solution changes or not.

Suppose that profit per pant increases to $25.How will this impact the optimal point and the value of the objective function value?

The optimal point will remain the samecan't tellincreasedecrease.

The objective function value will remain the samecan't tellincreasedecrease.

10 points

QUESTION 13

Suppose that profit per dress decreases to $14. Which one of the following statements is incorrect.

		The optimal-solution/optimum-point will remain the same.
		The OFV will remain the same.
		The OFV will decrease by 500 dollars.

10 points

QUESTION 14

Suppose that only 600 hours are available in the cutting department .

The Optimal solution will Remain Unchanged.IncreaseDecrease. The objective function value Remain Unchanged.IncreaseDecrease.

10 points

QUESTION 15

Suppose that only 690 hours are available in the packing department. How would the objective function value changes?

If it's unchanged enter zero.

if it's increased/decreased and the value can be calculated having only the sensitivity analysis report enter the new OFV.

If we need to resolve the problem to calculate the changes in OFV, enter 999.

10 points

QUESTION 16

Suppose we have to produce at least 50 more blouses than skirts. How does the objective function value changes?

If it's unchanged enter zero.

if it's increased and the value can be calculated having only the sensitivity analysis report enter the amount of increase as a positive number.

If it's decreased and the value can be calculated having only the sensitivity analysis report enter the amount of decrease as a negative number.

If we need to resolve the problem to calculate the changes in OFV, enter 999.

10 points

QUESTION 17

Suppose that the company has decided that there is no minimum number of garments they need to produce. Which one of the following options is correct.

		Optimal solution and OFV are unchanged.
		The optimal solution changes and the OFV is increased by an unknown amount.
		the optimal solution changes but the OFV remains the same.

10 points

QUESTION 18

Suppose that the company has unlimited availability for packing. In other words you can get as many hours of packing as you need (theoretically infinite). Which one of the follwoing options is correct?

		Optimal solution and OFV are unchanged.
		The optimal solution changes and the OFV is increased by an unknowm finite amount.
		The optimal solution changes and the OFV increases to positive infinity.