SOLUTION: I am having a problem with a setting up a linear programming word problem. Once I have the set up I am able to graph it fine. Please give assistance with the set up. A trip requi

Question 924161: I am having a problem with a setting up a linear programming word problem. Once I have the set up I am able to graph it fine. Please give assistance with the set up.
A trip requires bus and van rentals. Each bus has 40 seats and 1 handicapped seat. Vans have 8 seats and 3 handicapped seats. Rental costs is $350 for each van and $975 for each bus. If 320 seats and 36 handicapped seats are required, how many vehicles of each type should be rented to minimize cost?
Thank you for your help.
David
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
bus has 40 seats and one handicapp[ed seat.
each van 8 seats and 3 handicapped seats.
rental cost is $350 for the van and $975 for the bus.
need 320 regular seats and 36 yhandicapped seats
need to minimize cost.

x = number of buses
y = number of vans

objective function is 975*x + 350*y

you need a minimum of 320 regular seats.
bus has 40 regular seats and van has 8 regular seats.
equation for regular seats is 40x + 8y >= 320

you need a minimum of 36 handicapped seats.
bus has 1 handicapped seat and van has 3 handicapped seats.

equation for handicapped seats is 1x + 3y >= 36

x and y both have to be greater than or equal to 0.

your objective function is 975x + 350y which you want to minimize

your constraints are:

x,y >= 0
40x + 8y >= 320
1x + 3y >= 36

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