Lee washes the outsides of houses. It takes him 40 minutes to power wash a one-story home, and he uses 180 gallons of water. Power washing a two-story home takes 90 minutes and uses 300 gallons of water. Lee works no more than 40 hours each week, and he uses a maximum of 5 comma 000 gallons of water per week. He charges 90 dollars to wash a one-story home and 150 dollars to wash a two-story home. Lee wants to maximize his weekly washing income washing houses. Let x represent the number of one-story houses and y represent the number of two-story houses. What are the constraints for the problem?
Answer
A
40 x plus 90 y is less than or equal to 40 180 x plus 300 y is less than or equal to 5 comma 000 x is greater than or equal to 0 y is greater than or equal to 0
B
2 thirds x plus 3 halves y is less than or equal to 40 180 x plus 300 y is less than or equal to 5 comma 000 x is greater than or equal to 0 y is greater than or equal to 0
C
2 thirds x plus 180 y is less than or equal to 90 3 halves x plus 300 y is less than or equal to 150 x is greater than or equal to 0 y is greater than or equal to 0
D
2 thirds x plus 180 y is less than or equal to 90 3 halves x plus 300 y is less than or equal to 150 x is less than or equal to 40 y is less than or equal to 5 comma 000
Explanation
Convert the washing times to hours: 40 minutes is 2/3 hour, and 90 minutes is 3/2 hours. The weekly time limit gives (2/3)x + (3/2)y ≤ 40. The water limit gives 180x + 300y ≤ 5,000, and the numbers of houses must satisfy x ≥ 0 and y ≥ 0. These are the constraints in choice B.
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