Lee washes houses. It takes him 40 minutes to wash a one-story home, and he uses 18 gallons of water. Power washing a two-story home takes less than 90 minutes, and he uses 30 gallons of water. Lee works no more than 40 hours each week, and his truck holds 500 gallons of water. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his income washing one and two story 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?

Question

Mathematics

Dalia Zhang

28 May, 19:26

Lee washes houses. It takes him 40 minutes to wash a one-story home, and he uses 18 gallons of water. Power washing a two-story home takes less than 90 minutes, and he uses 30 gallons of water. Lee works no more than 40 hours each week, and his truck holds 500 gallons of water. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his income washing one and two story 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?

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Answers (2)

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Anne Mcdaniel · Answer 1

Given:

one-storey home : 40 minutes; 18 gallons of water

two-storey home : less than 90 minutes; 30 gallons of water.

Lee works 40 hours a week and his truck holds 500 gallons of water.

One constraint of the problem is the number of hours worked per week which is 40 hours only. Another constraint is the capacity of Lee's truck to hold water which is limited to only 500 gallons of water.

40 hours * 60 minutes/hour = 40 * 60 minutes = 2400 minutes.

40x + 90y < 2400

18x + 30y < 500

Dulce Huffman · Answer 2

It's D.

2/3x+3/2y=<40

18x+30y=<500

x=>0

y=>0