SOLUTION: A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to mix as many gallons as possible of color A and color B. Each gallon of color A requires 4 units

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to mix as many gallons as possible of color A and color B. Each gallon of color A requires 4 units       Log On


   



Question 1052614: A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to mix as many gallons as possible of color A and color B. Each gallon of color A requires 4 units of yellow dye and 1 unit of green dye. Each gallon of color B requires 1 unit of yellow dye and 6 units of green dye. Find the maximum number of gallons he can mix.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of gallons of A made and y be the number of gallons of B made.
Look at the units of yellow dye used for one gallon of A and B,
4x%2By%3C=32
Look at the units of green dye used,
x%2B6y%3C=54
Plot those lines and look at the values of the feasible region.
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(0,9):N=0%2B9=9
(6,8):N=6%2B8=14<--- Maximum number of gallons
(8,0):N=8%2B0=8