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, can the company build 20 child bikes and 6 adult bikes in a 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

9514 1404 393

Answer:

(a) No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Explanation:

Build times are 4 hours for a child's bike and 6 hours for an adult's bike. The number of build hours cannot exceed 120. This gives the first inequality:

4c +6a ≤ 120

Test times are 4 hours each. The number of test hours cannot exceed 100. This gives the second inequality:

4c +4a ≤ 100

This pair of inequalities matches choices A and C.

When we use c=20 and a=6, these become ...

4(20) +6(6) = 116 ≤ 120 . . . true

4(20) +4(6) = 104 ≤ 100 . . . false

The order cannot be built because the test time constraint cannot be met. This matches choice A.