You work at a local furniture manufacturer that specializes in producing chairs

Question

You work at a local furniture manufacturer that specializes in producing chairs and tables. Each table requires 4 units of wood and 3 hours to produce. Each chair required 2 units of wood and 1 hour to produce. Wood costs $10 per unit and labor costs $8 per hour. You can sell each table for $100 and each chair for $20. You can purchase at most 1,000 hours of labor per week. For contractual reasons, you must make at least twice as many chairs as tables. Setup the spreadsheet optimization model. How many chairs and tables will you produce to maximize profits? What is the maximum possible profit given the constants? What is the maximum total hourly wage we would be willing to pay for one additional hour of time?

Explanation / Answer

Table Chair Total $ $ Sale Value 100 20 Less:-Material Cost 40 20 Less:- Labour 24 8 Contribution per unit 36 -8 Production 200 400 Hours required 3 1 total 600 400 1000 Contribution 21600 -3200 18400 Let Table production = x units Chair = 2x units labour hours will be for table = 3x labour hours will be for chair = 2x Therefore 3x +2x = 1000 x =200 ie table = 200 and chair 400

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