Bob has a craft store that makes and sells birdhouses and mailboxes. Each birdhouse requires 3 hours of cutting materials and 1 hour of finishing. Each mailbox requires 4 hours of cutting and 2 hours of finishing. Bob will sell each birdhouse for $12 and each mailbox for $20. If Bob is restricted to 48 hours of cutting per week and 20 hours of finishing per week, how many of each item should he produce to maximize his revenue?

JetssheetaDumcb

JetssheetaDumcb

Answered question

2022-10-15

Bob has a craft store that makes and sells birdhouses and mailboxes. Each birdhouse requires 3 hours of cutting materials and 1 hour of finishing. Each mailbox requires 4 hours of cutting and 2 hours of finishing. Bob will sell each birdhouse for $12 and each mailbox for $20. If Bob is restricted to 48 hours of cutting per week and 20 hours of finishing per week, how many of each item should he produce to maximize his revenue?

Answer & Explanation

aitorarjolia

aitorarjolia

Beginner2022-10-16Added 11 answers

You can produce either 16 birdhouses or 10 mailboxes (the two extremes). 10 mailboxes produces 200 dollars while 16 birdhouses produces only 192 dollars.
Looking at the hours needed:
10 mailboxes will take 40 hours of cutting and 20 hours of finishing
16 birdhouses will take 48 hours of cutting and 16 hours of finishing.
You want to optimize this by using all the hours.
Bob can only have 48 cutting hours and 20 finishing hours. Since the mailboxes leaves Bob with extra cutting time, Bob can produce two birdhouses for every mail box.
9 mail boxes and 2 birdhouses will take 42 hours of cutting and 20 hours of finishing while producing 204 dollars. Continuing this pattern, you will find that the optimum number of each item will be:
6 mail boxes and 8 bird houses. This will take 6 4 + 8 3 = 48 cutting hours and 6 2 + 8 1 = 20 finishing hours. This uses up all hours and produces a total revenue of 216 dollars.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?