SOLUTION: Baking a try of corn muffins takes 4 c milk and 3 c wheat flour. A tray of bran muffins takes 2 c milk and 3 c wheat flour. A baker has 16 c milk and 15 c wheat flour. He makes $3

Algebra ->  College  -> Linear Algebra -> SOLUTION: Baking a try of corn muffins takes 4 c milk and 3 c wheat flour. A tray of bran muffins takes 2 c milk and 3 c wheat flour. A baker has 16 c milk and 15 c wheat flour. He makes $3       Log On


   

Question 103754This question is from textbook Algebra 2
: Baking a try of corn muffins takes 4 c milk and 3 c wheat flour. A tray of bran muffins takes 2 c milk and 3 c wheat flour. A baker has 16 c milk and 15 c wheat flour. He makes $3 profit per tray of corn muffins and $2 profit per tray of bran muffins. How many trays of each type of muffin should the baker make to maximize his profit? This question is from textbook Algebra 2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Baking a tray of corn muffins takes 4 c milk and 3 c wheat flour.
A tray of bran muffins takes 2 c milk and 3 c wheat flour.
A baker has 16 c milk and 15 c wheat flour.
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Let corn muffs be "c"; bran muffs be "b":
Milk Inequality: 4c + 2b <= 16
Flour Inequlity: 3c + 3b <= 15
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Solve each inequality for "c":
Milk: c <- (-1/2)b + 4
Flour:c <= -b + 5
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Graph these inequalities:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%2B4%2C-x%2B5%29
Comment: The area enclosed by b=0,c=0,and below the
intersecting lines is the set of possible values for
b and c. This is the solution set.
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He makes $3 profit per tray of corn muffins and $2 profit
per tray of bran muffins.
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Object function = 2b + 3c represents the total profit for
each combination of b and c in the solution set.
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Fo find the maximum profit test the vertices of the solution set in the
object function:
The vertices are:
(0,0) which gives 2*0+3*0 = 0 profit
(0,4) which gives profit = 2*0+3*4 = 12
(2,3) which gives profit = 2*2+3*3 = 13
(5,0) which gives profit = 2*5+3*0 = 10
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How many trays of each type of muffin should the baker make to maximize his profit?
two trays of bran and three trays of corn
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Cheers,
Stan H.