Home Styles 48
Linear Programing HELP!!?
I have a take home quiz with one problem but can solve it. Please help me.
“Surehold Shelving company produces two types of decorative shelves. The Olde English style takes 20 min. to assemble and 10 min. to finish. The Cool Contemporary style takes 10 min. to assemble and 20 min. to finish. Each day, there are 48 worker-hours of labor available in the assembly department and 64 worker-hours of labor available in the finishing department. To fulfill its commitments, the company must produce at least 200 shelving units per day. The cost of material for the Olde English shelf is $2.00 each. The cost of material for the Cool Contemporary shelf is $2.50 each. How many type of shelf should the company produce to minimize the cost of materials and still meet its production commitments?
Let x = number of Olde English style shelves produced
Let y = number of Cool Contemporary style shelves produced
Min C = 2x + 2.5y
s.t.
x + y >= 200 (must produce at least 200 shelving units a day)
20x + 10y <= 2840 (48 assembly hours -> 48hours*60 minutes/hour = 2840 assembly minutes per day)
10x + 20y <= 3840 (64 finishing hours -> 64hours*60minutes/hour = 3840 finishing minutes per day)
This was awkward to try and graph or explain that way, so I used linear programming software to solve it.
x = 84 Olde English style shelves produced, y = 116 Cool Contemporary style shelves produced, and C = 2(84) + 2.5(116) = $458 cost
Hope that helped. Good luck on your quiz.
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