Question

A small furniture company manufac- tures sofas and recliners. Each sofa requires 8 hours of labor and $180 in materials, while a recliner can be built for $105 in 6 hours. The company has 340 hours of labor available each week and can afford to buy $6750 worth of materials. How many recliners and sofas can be produced if all labor hours and all materials must be used?

Answer 1

30 and 20 respectively

Explanation:

Let the number of sofas to be built be s and the number of recliners be r.

For the time part, we have the following equation:

8s + 6r = 340

For the money part:

180s + 105r = 6750

Now let’s solve these equations simultaneously.

Let’s change the form of the second equation:

180s + 17.5(6r) = 6750

From the first equation, 6r = 340 - 8s

Insert this into the third equation

180s + 17.5(340-8s) = 6750

180s + 5950 - 140s = 6750

40s = 6750 - 5950

40s = 800

s = 20

Substitute the value into the first equation

8(20) + 6r = 340

6r + 160 = 340

6r = 180

r = 30