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Borges Machine? Shop, Inc., has a? 1-year contract for the production of 200,000 gear housings for a new? off-road vehicle. Owner Luis Borges hopes the contract will be extended and the volume increased next year. Borges has developed costs for three alternatives. They are? general-purpose equipment? (GPE), flexible manufacturing system? (FMS), and? expensive, but? efficient, dedicated machine? (DM). The cost data? follow:
|
?General-Purpose Equipment? (GPE) |
Flexible Manufacturing System? (FMS) |
Dedicated Machine? (DM) |
|
|
Annual contracted units |
200,000 |
200,000 |
200,000 |
|
Annual fixed cost |
$125,000 |
$225,000 |
$480,000 |
|
Per unit variable cost |
$16.00 |
$14.00 |
$13.00 |
The option GPE is best when the contracted volume is below ____ units (enter your response as a whole number)
The option FMS is best when the contracted volume is between ______ and _____ units (enter your response as a whole number)
The option DM is best when the contracted volume is over ____ units (enter your response as a whole number)
The state of Missouri has three major power-generating companies identified as 1, 2, and 3. During the months of peak demand, the Missouri Power Authority authorizes these companies to pool their excess capacity and to produce and distribute electricity to smaller independent power utilities that do not have generators large enough to handle all the demand. The supply, up to the excess capacity, is distributed on the basis of cost per kilowatt-hour transmitted.
The table below contains the costs (in cents, ¢) per kilowatt-hour (kwh) of transmitting power from the major companies 1, 2, and 3 to each of four different small independent companies W, X, Y, and Z. Also shown in the table are the demand and capacity for power in millions of kilowatt-hours (Mkwh).
TO
|
FROM |
W |
X |
Y |
Z |
Excess Capacity (Mkwh) |
|
1 |
12¢ |
4¢ |
9¢ |
5¢ |
45 |
|
2 |
2¢ |
1¢ |
4¢ |
7¢ |
50 |
|
3 |
8¢ |
12¢ |
6¢ |
6¢ |
55 |
|
Unfilled Demand (Mkwh) |
40 |
20 |
50 |
20 |
The problem is to determine the best way to allocate the power, in millions of kilowatt-hours, from the major companies to the small independents so as to keep the total distribution costs to the lowest that is possible.
(NOTE: Unit distribution costs entered in the body of the table above are listed in units of cents/kwh. Capacity and demand entered in the “rim cells†are both in units of Mkwh. HINT: In your modeling, convert the units costs to $/Mkwh.)
Define all the decision variables. Be explicit and specific (including units).
state the objective function in terms of the decision variables and the constraints of the situation described in terms of the decision variables.
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