Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of "4,700" bookshelf speakers and "5,500" floor speakers over the next two months, with the following delivery schedule: Model Month 1 Month 2
Bookshelf 2,800 1,900
Floor 2,200 3,300

Greenville estimates that the production time for each bookshelf model is 0.8 hour and the production time for each floor model is 1 hour. The raw material costs are $17 for each bookshelf model and $19 for each floor model. Labor costs are $29 per hour using regular production time and $40 using overtime. Greenville has up to 3,100 hours of regular production time available each month and up to 1,700 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 $12 per cabinet.

Required:
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. If required, round your answers to the nearest whole number.

  see attached

Explanation:

The total hours required to produce each month's order are ...

  Month 1: 0.8(2800) +1(2200) = 4440

  Month 2: 0.8(1900) +1(3300) = 4820

That is, orders for Month 2 require 20 more hours than are available. Both months require significant overtime.

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From this brief analysis, we learn that we must store a minimum of 20 hours worth of labor. We can minimize the storage cost by maximizing the hours of labor in each item stored. Floor models require 1 hour each, which is more than the labor requirement of a Bookshelf model. So, we should store 20 Floor models.

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Overtime is required in both months to fulfill the orders, so it doesn't really matter how the regular hours are spent. We can, for example, produce one entire order on regular time, and the other on overtime; or, we can split the hours so the product mix approximates the order mix. Either way, the labor cost will be the same.

We choose to spend the 3100 regular hours producing 1575 Bookshelf models, and 1840 Floor models.

Then the overtime hours can be spent making up the difference from the total for the month.

The attachment shows the allocation of quantities, hours, and labor dollars. The total (minimized) production and storage cost is shown at lower right.

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