Question

Sam and Avery are making small and large birdhouses for an upcoming craft show. They will sell the small birdhouses for $10 and the large birdhouses for $15. They want to make as much money as possible. It takes Sam 3 hours to build the small houses and 5 hours to build the large ones. He only has 24 hours to work on them. Avery only has time to decorate 12 birdhouses of either size before the show. How many small and large birdhouses should they make? How much money will they make?

Answer 1

Answer:

They should make 8 small ones and 12 large ones.

$260 they will make in total.

Step-by-step explanation:

They want to make as much money as possible.

Small bird house gives them $10 and large birdhouse give them $15.

Avery has time to decorate 12 birdhouse of either size.

Hence, to maximize the earning, Avery should build 12 large ones.

Sam can make any of the combination below in 24 hours.

4 Large and 1 small bird house, which will make $4 \times 15 + 10 = 70$

3 Large and 3 small bird house, which will make $3 \times15 + 3 \times10 = 75$

2 Large and 4 small bird house, it will gain $2 \times15 + 4 \times10 = 70$

1 Large and 6 small bird house, it will make $1 \times15 + 6 \times10 = 75$

8 small bird house, which will gain $8\times10 = 80$

The profit will be maximize if Sam build 8 small bird houses.

Thus, they will make $80 + 12\times15 = 260$.