Answered Essay: Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,300 bookshelf s

Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,300 bookshelf speakers and 4,100 floor speakers over the next two months, with the following delivery schedule:

Model Month 1 Month 2
Bookshelf 2,100 1,200
Floor 1,500 2,600

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 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 2,400 hours of regular production time available each month and up to 1,000 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. If required, round your answers to the nearest whole number.

Regular Time Manufacture
Model Month 1 Month 2
Bookshelf xx xx
Floor xx xx
Overtime Manufacture
Model Month 1 Month 2
Bookshelf xx xx
Floor xx xx

Expert Answer

 

This is a production scheduling problem in which we need to minimize the cost

The decision variables will the regular production for two models in each month and overtime production for models in each month

Objective function: Min Total COst = Regular Production Cost + Overtime Production Cost + Raw Material COst + Inventory COst

Constraints: Regular time <= 2400

Overtime <= 1000

Ending Inventory >= 0

All decision variables will be integer and will be greater than zero

Hence, production plan is:

Model Month1 Month2
Regular Production Bookshelf 2100 1200
Floor 930 1560
Overtime Production Bookshelf 0 0
Floor 610 1000
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