Mann Enterprises is a Houston manufacturer of tables and accessories for personal computers. The company is caught in a vicious cross fire between rapidly dropping market prices from competitors worldwide for its products and stable domestic costs for its materials. The 15 different products noted below must be scheduled to maximize profits or there will be no jobs and no firm in another 3 months. Your job as the new OM graduate is to address the issues raised this morning by Laura Mann, the president, in an emergency meeting in her office. Without being told soexplicitly, you conclude that if you don't get the schedule done accurately and in a timely manner, you will be history. To yourrelief, the industrial engineers and accountants have provided the data shown below. The issues, as recorded in your notes, are indented in (a) through (f).

Product	Steel Alloy Required (Lb.)	Plastic Required (Sq. Ft.)	Wood Required (Bd. Ft.)	Aluminum Required (Lb.)	Formica Required (Bd. Ft.)	Labor Required (Hr.)	Minimum Monthly Demand (Units)	Contribution to Profit
A158	long dash—	0.4	0.7	5.8	10.9	3.1	long dash—	$18.79
B179	4	0.5	1.8	10.3	2.0	1.0	20	6.31
C023	6	long dash—	1.5	1.1	2.3	1.2	10	8.19
D045	10	0.4	2.0	long dash—	long dash—	4.8	10	45.88
E388	12	1.2	1.2	8.1	4.9	5.5	long dash—	63.00
F422	long dash—	1.4	1.5	7.1	10.0	0.8	20	4.10
G366	10	1.4	7.0	6.2	11.1	9.1	10	81.15
H600	5	1.0	5.0	7.3	12.4	4.8	20	50.06
I701	1	0.4	long dash—	10.0	5.2	1.9	50	12.79
J802	1	0.3	long dash—	11.0	6.1	1.4	20	15.88
K900	long dash—	0.2	long dash—	12.5	7.7	1.0	20	17.91
L901	2	1.8	1.5	13.1	5.0	5.1	10	49.99
M050	long dash—	2.7	5.0	long dash—	2.1	3.1	20	24.00
N150	10	1.1	5.8	long dash—	long dash—	7.7	10	88.88
P259	10	long dash—	6.2	15.0	1.0	6.6	10	77.01
Availability per month	980	400	600	2,500	1,800	1,000

a) Only product _____ is not produced.

b) Clearly explain the meaning of each shadow price.

Since the shadow price for constraints C2, C5, C6, C7, C11, C18, and C20 is 0, these are _______ (nonbinding or binding) constraints.

The shadow price for constraint C1 is $2.71, which is the benefit of _____ (increasing or reducing) the right-hand side by one unit.

The shadow price for constraint C19 is $29.24, which is the benefit of ______ (increasing or reducing) the right-hand side by one unit.

c) A number of workers interested in saving money for holidays have offered to work overtime next month at a rate of $12.50 per hour. What should the response of management be?

The workers should work ____ hours per month overtime (enter your response as a whole number).

d) Two tons of steel alloy are available from the overstocked supplier at a local cost of $8,000.

The steel ____ (should or should not) be purchased.

If 44 pounds of it are purchased, the total profit will increase by $ _____ (round your response to two decimal places).

e) The accountants have just discovered that an error was made in the contribution to profit for product N150. The correct value is actually $8.88. The ________should be corrected.

The corrected objective function is (round your responses to two decimal places):

Maximize Z = 18.79XA + 6.31XB + 8.19XC + 45.88XD + 63.00XE+ 4.10XF + 81.15XG + 50.06XH + 12.79XI + _____XJ + _____XK + ____XL + 24.00XM + _____XN + _____XP

Data Table Original Coefficient Reduced Optimal Value Product Lower Limit Upper Limit Cost 1.32373 18.79 - Infinity 20.11373 XA XB 20 6.31 - Infinity 52.49662 Xc 8.19 - Infinity 34.64475 10 Xp 45.88 - Infinity 48.41532 10 XE 63 59.01673 77.38298 11.507 XF 4.1 - Infinity 31.47013 20 XG 81.15 - Infinity 115.1911 10 XH 50.06 - Infinity 82.73582 20 X, 12.79 - Infinity 24.539 50 X, 15.88 - Infinity 26.7216 20 XK 17.91 - Infinity 27.28386 20 49.99 47.34072 56.43208 XL XM 54.945 20 24 - Infinity 53.243 XN 88.88 80.82936 126.4764 12.202 Xp 77.01 - Infinity 125.8801 10 Print Done