Mann Enterprises is a Houston manufacturer of tables and accessories for personal computers. The company is caught
Question:
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
Expert Answer:
