Operation Management Case Solution
Question 1
Sofa Products | Table Products | Chair Products | ||
Production | 60 | 0 | 0 | |
Unit Profit | 320 | 275 | 190 | |
Sofa Products | Table Products | Chair Products | Used | |
Sofa | 7 | 12 | 6 | 420 |
Table | 5 | 0 | 9 | 300 |
Chair | 4 | 7 | 5 | 240 |
Profit Optimization | 19200 |
From the following analysis, it is determined that in order to maximize profit over the week, the linear programming model is used to calculate the expected requirements of the products to cover the optimal value. Conclusively, only the production of chairs will be required to boost the performance of Hickory Cabinet and Furniture Company.
It indicates that the minimum level of productions of chairs should be 60 per week to produce the net value of profit optimization. This will tend to increase by the same margin if such strategy will use over the number of selected weeks of production.
It is also determined that the customers may use each of the products over the week and shows that it will likely boost according to the strategy of profit maximization. The net results, however, show that such increase will hinder the production capability to produce enough chairs. Therefore, if the company will maximize the production, then it should also increase the same level of profits.
Question 2
Special | Mountain Dark | Mill Regular | |
Production | 33.2 | 20.5 | 138.1 |
Unit Profit | 3.8 | 3.0 | 2.2 |
Special | Mountain Dark | Mill Regular | Used | |
Brazilian | 0.2 | 1 | 0.6 | 110 |
Mocha | 0.83 | 0.55 | 0.14 | 57.62 |
Colombian | 1.45 | 0.58 | 0.15 | 80.00 |
Mild | 0.17 | 0.17 | 1.02 | 150.00 |
Profit Optimization | 495.73793 |
The results under the linear programming model shows that the average consumption of Brazilian coffee in all the packages will be 110 weekly, whereas Mocha will generate high consumption value due to high price per pound. On the other side, Colombian shows moderate utilization rate over the week. Lastly, Mild will be successful due to its low price range per pound of the coffee.
According to the current analysis, in order to meet the profit optimization value, every product package should be produced in addition to the proposed profits. According to the lowest price level, Mill Regular should produce at least 138.1 per week in order to meet the requirement. The other two categories should not exceed the Mill regular because they will utilize high cost of production. In conclusion, profit optimization will be achieved if certain additional production facilities will incur.
Question 3
Denim | Corduroy | |
Production | 0 | 159.375 |
Unit Profit | 2.25 | 3.1 |
Raw material for yard | Time require per yard | Used | |
Denim | 5 | 3 | 478.125 |
Corduroy | 7.5 | 3.2 | 510 |
Profit Optimization | 494.0625 |
From the results, it is expected that 478 denims per week due to the nature of traditional product that can be sold at any time of the year. Corduroy is a unique product of the company, which has limited demand over the season. According to the case, this product should be used more than the Denim if such season will be favorable to the company.
It is concluded that in order to meet the demand of profit maximization of the company, an additional production of 159 of Corduroy per week should be implemented. This will allow to boost profit margins with respect to the changes in the production level.
Slope | |||
5X+7.5Y≤ 700 | X=0 | 93.33333333 | (0,93) |
Y=0 | 140 | (140,0) | |
3X+3.2Y≤ 510 | X=0 | 159.375 | (0,159) |
Y=0 | 170 | (170,0) |
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240 | ||||||
210 | ||||||
180 | ||||||
150 | ||||||
120 | ||||||
90 | ||||||
60 | ||||||
30 | ||||||
30 60 | 90 120 | 150 180 | 210 240 |
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