Question

Comfort-by-Design Furniture produces chairs and sofas. Each chair requires 20 ft of wood, 1 lb of foam rubber, and 2 yd² of fabric. Each sofa requires 100 ft of wood, 50 lb of foam rubber, and 20 yo² of

fabric. The manufacturer has in stock 2000 ft of wood, 550 lb of foam rubber, and 240 yd² of fabric. The chairs can be sold for $150 each and the sofas for $525 each. How many of each should be
produced in order to maximize income? What is the maximum income?

Answer 1

To maximize income, we need to determine the number of chairs and sofas that should be produced. Using linear programming, the solution is 60 chairs and 4 sofas, resulting in a maximum income of $12,300.

Step-by-step explanation:

To maximize income, we need to determine the number of chairs and sofas that should be produced. Let's use the following variables:

C = number of chairs

S = number of sofas

Now, we can set up the constraints:

20C + 100S ≤ 2000 (constraint for wood)

1C + 50S ≤ 550 (constraint for foam rubber)

2C + 20S ≤ 240 (constraint for fabric)

Next, we can set up the objective function:

Income = 150C + 525S

Using linear programming, we can solve this problem. The solution will give us the number of chairs and sofas that should be produced to maximize income:

Number of chairs (C) = 60

Number of sofas (S) = 4

To find the maximum income, substitute the values of C and S into the objective function:

Maximum Income = 150(60) + 525(4) = $12,300