Question

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 5 child bikes and 15 adult bikes in the week.
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answer 1

Answer:

  Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Step-by-step explanation:

The constraint on build hours is ...

  4c +6a ≤ 120

The constraint on test hours is ...

  4c +4a ≤ 100

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The latter constraint requires the total number of bikes (c+a) be at most 25. The order under consideration is for 20 bikes, so easily meets this constraint.

The constraint on build hours has "c-" and "a-intercepts" of 30 and 20, respectively. That is, if all of the the bikes being built were adult bikes, at most 20 of them could be built.

The two constraints together tell you that any order of 20 or fewer bikes can be satisfied. The order in question is for 20 bikes, so can be built.