Three Scenarios of Kamm Industry

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When we look at the sensitivity report below, we can find the interesting thing that the Final Value of carpet 2 is same as its Allowable Decrease, which means this carpet can totally be eliminated.

If we eliminate this carpet, the money we will save equals to the shadow price times its Final Value (money saved on carpet 2 = shadow price * allowable decrease= $2.6749 * 52000=$138,840)

Compared with the total cost we spend on carpet 2, we can find we actually save more money if we stop producing carpet 2.

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Table 9.3 basic scenario sensitivity report

Scenario 10:

With recent good performance in the global economy, our client Kamm witnesses an excellent performance of the carpet market. In order to make more profit, the management layer of Kamm come to consult which type of carpet should Kamm encourage its sales force to sell more if the carpet in orders 5 through 15 all sell for the same price?

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Table 10.1 basic scenario sensitivity report

When we compare the shadow price and the allowable increase in this sensitivity report, we can find carpet 14 has the lowest Shadow Price and a promising Allowable Increase. With lowest Shadow Price, carpet 14 will cost least and make most profit when it sells at the same price as other carpets. And it has a promising Allowable Increase, which means it has the potential to be encouraged selling target.

Scenario 11/12:

The management layer of Kamm is very attentive to the market performance, and they also change their selling strategy after each change, including both market change and resource change. After a recent adjustment to the looms, they found that the cost of carpet order 1 and order 15 has changed. Cost of carpet order 1 increased to $2.80 per yard and carpet order 15 decreased to $1.65 per yard. Then their strategy group wants to change the production amount of these two orders in order to make the best profit.

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Table 11/12.1 Orders and Demands

Decision Variables:

Let Di = Yards of carpet order i produced by Dobie

Let Pi = yards of carpet order i produced by Pantera

Let Si = yards of carpet order i subcontracted

1

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Table 11/12.2 Decision Variables of All the Orders

Constrains:

- Di+Pi+Si >= Demand(i),1

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Table 11/12.3 Time Constraints of Different Looms

- D1/4.51+D2/4.796+....

- P5/5.145+....

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Table 11/12.4 Time Cost on All Carpets for Each Looms

Objective:

Min(The cost of all the carpet orders)= SUMPRODUCT(amount D, cost D) +SUMPRODUCT(amount P, cost P)+SUMPRODUCT(amount buy, cost buy)

Solver results:

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Table 11/12.5 Solver Result of This Scenario

Analysis and answer report:

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Table 11/12.6 Sensitivity Report of Order 1 and 5

Answer to the question:

11. Yes, the optimal solution change. Because according to the sensitivity report, this change is out of the allowable change.

Then after we re-run the solver and find that if the cost of carpet 1 increases, in order to minimize the cost, we don't buy carpet 1 anymore.

12. No, the optimal solution doesn't change. Because according to the sensitivity report, 1.65 is within the change.