Question

AKS 18/19 A travel agent is arranging a private cruise. The agent can arrange for, at most, 40 people to go on the trip. The trip cannot be finalized unless there are at least 12 men and 15 women committed to the cruise. The agent will make $26 profit per man and $14 profit per woman. What are the constraints for this situation?

Answer 1

M + W <= 40

M >= 12

M >= 15

Total profit = $26 * M + $14 * W

Explanation:

Let the number of men be denoted by M

number of women be denoted by W

Maximum no of people that can go one trip = 40

Therefore representing it mathematically we have

M + W <= 40 -------------- CONSTRAINT 1

Minimum number of men needed on trip = 12

Therefore representing it mathematically we have

M >= 12 CONSTRAINT 2

Minimum number of women needed on trip = 15

Therefore representing it mathematically we have

M >= 15 CONSTRAINT 3

profit on 1 man = $26

profit on M men = $26 * M

profit on 1 woman = $14

profit on M men = $14 * W

Total profit combining for men and women =

$26 * M + $14 * W -------------CONSTRAINT 4

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writing together all the constraint

M + W <= 40

M >= 12

M >= 15

Total profit = $26 * M + $14 * W