Question 1

The Ace Manufacturing Company (AMC) produces two product lines: SuperAce and RegularAce. Resource requirements for production are given below.

Product Line	Profit per Unit	Assembly Time (hours)	Painting Time (hours)	Inspection Time (hours)
RegularAce	$50	1.2	0.8	0.2
SuperAce	$75	1.6	0.9	0.2

AMC has a capacity of 1600 hours of assembly time, 700 hours of painting time, and 300 hours of inspection time available each week. Suppose that demand for both products are unlimited, but AMC must produce at least 90 units of SuperAce and 150 units of RegularAce to satisfy contractual obligations. We are given the following linear program:

Maximize 50X₁ + 75X₂ (total weekly profit)

Subject to 1.2X₁ + 1.6X₂ <= 1600 (assembly time)

0.8X₁ + 0.9X₂ <= 700 (painting time)

0.2X₁ + 0.2X₂ <= 300 (inspection time)

X₁ >= 150 (RegularAce contract)

X₂ >= 90 (SuperAce contract),

where X₁ is the number of units of RegularAce produced each week and X₂ is the number of units of SuperAce produced each week. Both X₁ andX₂ are non-negative and can be non-integers.

Adjustable Cells
		Final	Reduced	Objective	Allowable	Allowable
	Cell	Value	Cost	Coefficient	Increase	Decrease
	X1	150	0	50	16.6667	1E+30
	X2	644.4444	0	75	1E+30	18.75
Constraints
		Final	Shadow	Constraint	Allowable	Allowable
	Cell	Value	Price	R.H. Side	Increase	Decrease
	Assembly time	1211.1111	0	1600	1E+30	388.8889
	Painting time	700	83.3333	700	218.75	499
	Inspection time	158.8889	0	300	1E+30	141.1111
	RegularAce contract	150	-16.6667	150	623.75	150
	SuperAce contract	644.4444	0	90	554.4445	1E+30

Use the Excel output above to answer the following questions with justification. Correct the answers to 2 decimal places if necessary.

1. What is the optimal weekly profit, as given by the Excel output?

2. At the optimal solution, which of the resource(s) is fully utilized?

3. If the capacity of assembly time increases from 1600 to 1601 hours, what is the optimal profit of AMC?

4. If the capacity of painting time decreases from 700 to 600 hours, what is the optimal profit of AMC?

5. If the contractual obligation for RegularAce increases by ten unit, what is the optimal profit of AMC?

6. Suppose AMC can purchase extra capacity of assembly time. Should AMC purchase an additional hour of assembly time if it can be purchased at $5 per hour? What is the effect on the optimal profit of AMC?

7. Suppose AMC can purchase extra capacity of painting time. Should AMC purchase an additional hour of painting time if it can be purchased at $10 per hour? What is the effect on the optimal profit of AMC?

8. Suppose AMC can sell their capacity of inspection time (i.e. reduce their capacity by renting out their equipment). Should AMC sell one hour of inspection time if it can be sold at $8 per hour? What is the effect on the optimal profit of AMC?

1. If the profit per unit of SuperAce decreases from $75 to $55, what is the optimal profit of AMC?

10. If the profit per unit of RegularAce increases from $50 to $65, what is the optimal profit of AMC?