Question

A furniture company makes large and small chairs. A small chair takes 30 minutes of machine time and 75 minutes of labor to build. A large chair takes 40 minutes of machine time and 80 minutes of labor to build. The company has 57 hours of labor time and 26 hours of machine time available each day. How many of each type of chair is built in a day?

Answer 1

Let the number of large chairs be x and small chairs be y
40x + 30y = 26 x 60 = 1,560 . . . . (1)
80x + 75y = 57 x 60 = 3,420 . . . . (2)

(1) x 2 => 80x + 60y = 3,120 . . . . (3)

(2) - (3) => 15y = 300 => y = 300/15 = 20

From (2), 80x + 75(20) = 3,420 => 80x + 1,500 = 3,420 => 80x = 3,420 - 1,500 = 1,920 => x = 1,920/80 = 24

Therefore, the company should produce 24 large chairs and 20 small chairs.