Greenville Cabinets received a contract to produce speaker cabinets for a major
ID: 470041 • Letter: G
Question
Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,700 bookshelf speakers and 4,500 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 $12 for each bookshelf model and $14 for each floor model. Labor costs are $24 per hour using regular production time and $35 using overtime. Greenville has up to 2,600 hours of regular production time available each month and up to 1,200 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 $7 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.
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Model Month 1 Month 2 Bookshelf 2,300 1,400 Floor 1,700 2,800Explanation / Answer
There are two types of Speakers and two types of Manufacture to meet demands of two months.
Therefore as mentioned in the question there are eight decision variables, and objective is to have the minimum total cost of production and storage. Costs are in terms of raw materials and labour cost (varying for regular and overtime used), and cost of storage. Constraints are in terms of demand and available time (Regular & Overtime).
Let BR1 and BR2 represents the number of Bookshelf speakers produced during regular time in the months 1, and 2 respectively and BO1, and BO2 during overtimes in the 1st and 2nd month respectively. Similarly FR1, FR2, FO1, and FO2 represents the number of Floor speakers corresponding to regular and overtime production during 1st and 2nd months respectively.
Bookshelf speaker requires .7 hours, therefore labour cost during regular time is $16.8 (24*.7) and during overtime is $24.5 (35*.7). Floor speaker takes 1 hour therefore corresponding labour costs are $24 and $35.
Construction of the linear programming problem in excel is as follows:
As per the solution there is no need to have storage as this will add to the cost.
Total minimum cost is $298,350 for production only.
Decision variables BR1 BR2 BO1 BO2 FR1 FR2 FO1 FO2 SB1 SF1 D.V.Values 2300 1320 1.19E-08 80 990 1676 710 1124 0 0 Objective function Unit Production cost 28.8 28.8 36.5 36.5 38 38 49 49 Unit Storage cost 0 0 0 0 7 7 Total Prod. cost 298350 Total storage cost 0 Total cost Min. 298350 Constraints Demand Bookshelf month1 1 0 1 0 2300 2300 Bookshelf month2 1 1 1400 1400 Floor month1 1 1 1700 1700 Floor month2 1 1 2800 2800 Production hours Regular month1 0.7 1 2600 2600 Overtime month1 0.7 1 710 1200 Storage quantityBo 0 1400 Regular month2 0.7 1 2600 2600 Overtime month2 0.7 1 1124 1200 Storage quantityFl 0 2800Related Questions
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