A furniture manufacturer makes a mix of desks (D) and chairs (C). Each desk uses

ID: 2738996 • Letter: A

Question

A furniture manufacturer makes a mix of desks (D) and chairs (C). Each desk uses three units of wood, and each chair uses five units of wood. Each desk generates a profit of $55, and each chair generates $35 in profit. Production facilities are setup in such a way that the number of chairs produced must be exactly 1.5 times the number of desks. The plant capacity is 100 pieces of furniture a day. There are 190 units of wood available per day. The furniture manufacturer wishes to find the optimal daily production combination of desks and chairs in order to maximize profit in a given day.

State the Objective function mathematically.

State the constraints mathematically.

Setup the model in Excel and use Solver to determine the optimized solution.

How many desks should be produced?

How many chairs should be produced?

What is the overall daily profit?

Explanation / Answer

Details

Desks (D)

Chairs (c )

Require the wood for produce of each unit

3 units

5 units

Profit of each unit produce (a)

$ 55.00

$ 35.00

Number of units produced (b)

25.33

22.8

Require the wood for produce of total units (c )

114

Total profit (d) = (a) *(b)

$ 1,393.15

$ 798.00

The objective function or key factor is available of wood.

Desks are produced 25 units.

Chairs are produced 23 units.

The overall daily profit is ($1,393.15 + $798) = $2,191.15.