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16 September, 14:01

A furniture cabinet maker produces two types of cabinets that house and hide plasma televisions. The Mission-style

cabinet requires $340 in materials and 15 labor hours to produce, and it yields a prot of $910 per cabinet. The Rustic-style

cabinet requires $430 in materials and 20 hours to produce, and it yields a prot of $1,200. The rm has a budget of

$30,000 to spend on materials. To ensure full employment, the rm wishes to plan to maximize its prot but at the same

time to keep all 30 workers fully employed, so all 1,200 available labor hours available must be used. What is the best

combination of furniture cabinets to be made?

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Answers (1)
  1. 16 September, 17:11
    0
    The maximum profit is $72,800 with 80 cabinets of Mission-style and no cabinets of Rustic-style to be used

    Explanation:

    Let the furniture cabinet maker produce x Mission-style cabinets and y Rustic-style cabinets

    Objective function: Maximize profits

    Profit yielded by a Mission-style cabinet = $910

    Profit yielded by x Mission-style cabinets = $910 * (x)

    Profit yielded by a Rustic-style cabinet = $1200

    Profit yielded by y Rustic-style cabinet = $1200 * (y)

    Objective function: Max (910x + 1200y)

    Subjected to Constraints

    Labor Hours: No of hours required to produce a Mission-style cabinet = 15

    No of hours required to produce a Rustic-style cabinet = 20

    Total Labor Hours = 1200

    Constraint 1) 15 * (x) + 20 * (y) = 1200

    Budget = $30,000

    Cost of materials for a Mission-style cabinet = $340

    Cost of materials for a Rustic-style cabinet = $430

    Constraint 2) 340 * (x) + 430 * (y) < = 30000

    Constraint 3) x and y > = 0

    Put these constraints in Excel solver, we obtain the maximum profit as $72,800 with 80 cabinets of Mission-style and no cabinets of Rustic-style to be used
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