Question

Can someone explain how to set up constraints for this linear programming problem?

Michael Thomas, the manager of a paint store, is mixing paint for a spring sale. There are 32 units of yellow dye, 54 units of brown dye, and an unlimited supply of base paint available. Mr.Thomas plans to mix as many gallons as possible of Autumn Wheat and Harvest Brown paint. Each gallon of Autumn Wheat requires 4 units of yellow dye, and 1 unit of brown dye. Each gallon of Harvest Brown paint requires 1 unit of yellow dye and 6 units of brown dye. Find the maximum number of gallons of paint that Mr.Thomas can mix.

Answer 1

let A be Autumn wheat, H be Harvest brown

yellow dye:
4A +H <= 32

brown dye:
A +6H <= 54

maximize objective function "G" for gallons
G = A+H

Answer 2

I am confused, why is it not 5a +H<= 32 ? the total amount of yellow paint?

Answer 3

"A" takes 4 units of yellow not 5

Answer 4

just kidding I see it, one is the constraints for Autumn Wheat and the other for Harvest brown right?

Answer 5

the constraints are on the amount of yellow dye and brown dye

Answer 6

how much yellow dye/brown dye you use is based on how many gallons of "A" and "H"

Answer 7

Is the constraint on the maximum equation 86?

Answer 8

??
how do you get A+H = 86

Answer 9

A+H <=86 because there is only 86 units of dye

Answer 10

oh i see
you are still confusing gallons of paint with units of dye
A is gallons of Autumn wheat paint...NOT units of yellow/brown dye

Answer 11

there is no constraint on "G = A+H" because we dont know what it is....thats what we are solving for, the maximum possible number of gallons

Answer 12

so there are only 2 constraints? yellow and brown dye?

Answer 13

correct

Answer 14

OH okay :) thank you

Answer 15

yw