Assignment- Linear Programming
Kaplan Computers manufactures high end computer systems for the graphics design industry. At the present time, the company makes three computers with the following characteristics:
|
|
Computer 1
|
Computer 2
|
Computer 3
|
|
Unit selling price
|
$12,000
|
$11,000
|
$10,000
|
|
Unit variable cost
|
7,000
|
8,500
|
8,000
|
The manufacture of the computers requires three major activities during their assembly. There is limited capacity for each resource. The following table shows the amount of each resource consumed by each computer and the capacity available of that resource.
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|
Computer 1
|
Computer 2
|
Computer 3
|
Capacity
|
|
Resource A
|
3
|
4
|
6
|
24,000
|
|
Resource B
|
5
|
6
|
2
|
36,000
|
|
Resource C
|
8
|
3
|
2
|
32,000
|
Additional resources are available, but need to be purchased in 1,000 unit increments.
Required:
1. Assume that demand for each product exceeds the capacity available. Choose a production plan that maximizes contribution.
2. Assume that, for marketing purposes, Kaplan needs to manufacture at least 300 units of each product. Choose a production plan that maximizes contribution.
3. Refer to the situation as describe in part 2. By how much would the contribution increase if an additional unit of Resource A became available?
4. Refer to the situation as described in part 2. You can purchase extra units of Resources A, B and C as follows:
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|
Amount Available
|
Cost per 1,000 units
|
|
Resource A
|
3,000
|
$22,000
|
|
Resource B
|
2,000
|
$250,000
|
|
Resource C
|
1,000
|
$625,000
|
How much of each resource should Kaplan acquire? By doing so, what is the incremental contribution that can be obtained? What quantity of each computer will now be made?
5. In addition to the extra resources available as described in part4, a different supplier has offered to supply an additional 1,000 units of Resource C, at a cost of $750,000. Should Kaplan accept the offer or not? You must biuy all 1,000 units or none at all. Provide quantitative support.