Greenville Cabinets received a contract to produce speaker cabinets for a major

Question

Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3300 bookshelf speakers and 4100 floor speakers over the next two months, with the following delivery schedule:

Greenville estimates that the production time for each bookshelf model is 0.7 hour and the production time for each floor model is 1 hour. The raw material costs are $10 for each WWW.YAZDANPRESS.COM bookshelf model and $12 for each floor model. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2400 hours of regular production time available each month and up to 1000 additional hours of overtime available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of $5 per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs.

Explanation / Answer

Hours available in each month = 2400 regular and 1000 overtime = 3400 hours

Hours required for production in month 1 = 2100 x 0.7 + 1500 x 1 = 1470 + 1500 = 2970 hours

Hours required for production in month 2 = 1200 x 0.7 + 2600 x 1 = 840 + 2600 = 3440 hours

This means that production of 40 hours will have to be done in the first month to adjust for the additional hours of the next month as next month the hours available would be 3400.

It does not matter whether you produce one model in the regular time or the overtime it will take a total of 2970 hours to produce 2100 bookshelf model and 1500 floor model. Hence the total cost of labor remains the same. We produce the entire 2100 bookshelf model and 930 floor models in the regular time available and the remaining 570 floor models in the overtime. Now from the 430 overtime hours remaining in the first month we will have to utilize 40 hours to either produce bookshelf model or floor model. If we produce bookshelf model we will produce 40 / 0.7 = 57 models and the storage cost will be 5 x 57 = $285 and if we produce floor model we will produce 40 / 1 = 40 models and the storage cost will be 5 x 40 = $200. Hence we will produce the floor model as the storage cost is minimal. So, in the first month the production would be the entire 2100 bookshelf models and 930 floor models in the regular time and 570 remaining floor models and 40 additional floor models for next month in the overtime. In the next month there would be no storage cost hence the entire 1200 bookshelf models and 1560 floor models can be produced in the regular time and the remaining 1000 floor models can be produced in the overtime.

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