Mathematics

Question

Sam & Avery are making small and large birdhouses for a craft show. Small houses sell for $10 and large houses sell for $15. It takes Sam 3 hours to build small houses and 5 hours to build large houses. He only has 24 hours of building time. Avery only has time to decorate 12 houses of either size. How many small & large houses should be made to make the most money?

If Sam had 30 days instead of only 24 hours and Avery had time to decorate 100 birdhouses instead of only 12, discuss solution methods you used and why.

1 Answer

  • Answer:

    • 8 small houses; 0 large houses
    • 80 small houses; 0 large houses

    Step-by-step explanation:

    a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.

    Sam should make 8 small houses and 0 large houses in 24 hours.

    __

    b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.

    _____

    If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.

    If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.

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