Question

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?

Answer 1

Answer:

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