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 10 child bikes and 12 adult bikes in a week. (2 points) 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:

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

Explanation:

Try the numbers in the constraints to see if they work.

Build hours:

(4 h/child bike)(10 child bikes) = 40 hours

(6 h/adult bike)(12 adult bikes) = 72 hours

total build hours: 40 +72 = 112, less than 120; constraint is met

Test hours:

(4 h/child bike)(10 child bikes) = 40 hours

(4 h/adult bike)(12 adult bikes) = 48 hours

total test hours: 40 +48 = 88, less than 100; constraint is met

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Both constraints are met, so the order can be filled.