A company produces two products made from aluminum and copper. The table below gives the unit requirements, the unit production man-hours required, the unit profit and the availability of the resources (in tons).

	Aluminum	Copper	Man-hours	Unit Profit
Product 1	1	0	2	50
Product 2	1	1	3	60
Available	10	6	24

The Management Scientist provided the following solution output:

Objective Function Value = 540.000

VARIABLE	VALUE	REDUCED COST
X1	6.000	0.000
X2	4.000	0.000

CONSTRAINT	SLACK/SURPLUS	DUAL PRICE
1	.000	30.000
2	2.000	0.000
3	0.000	10.000

RANGES IN WHICH THE BASIS IS UNCHANGED:

		OBJ. COEFFICIENT RANGES
VARIABLE	CURRENT COEFFICIENT	ALLOWABLE INCREASE	ALLOWABLE DECREASE
X1	50.000	10.000	10.000
X2	60.000	15.000	10.000

		RIGHTHAND SIDE RANGES
CONSTRAINT	CURRENT RHS	ALLOWABLE INCREASE	ALLOWABLE DECREASE
1	10.000	2.000	1.000
2	6.000	INFINITY	2.000
3	24.000	2.000	4.000

a.	What is the optimal production schedule?
b.	Within what range for the profit on product 2 will the solution in (a) remain optimal? What is the optimal profit when c2 = 70?
c.	Suppose that simultaneously the unit profits on x1 and x2 changed from 50 to 55 and 60 to 65 respectively. Would the optimal solution change?
d.	Explain the meaning of the "DUAL PRICES" column. Given the optimal solution, why should the dual price for copper be 0?
e.	What is the increase in the value of the objective function for an extra unit of aluminum?
f.	Man-hours were not figured into the unit profit as it must pay three workers for eight hours of work regardless of the number of man-hours used. What is the dual price for man-hours? Interpret.
g.	On the other hand, aluminum and copper are resources that are ordered as needed. The unit profit coefficients were determined by: (selling price per unit) - (cost of the resources per unit). The 10 units of aluminum cost the company $100. What is the most the company should be willing to pay for extra aluminum?

Answer rating: 100% (QA)

a X 1 6 and X 2 4 bLower range Objective coeffAllowable decrease thus 601050 Upper rangeObjectiv... View the full answer