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

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) (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.
--------------------------------
Let corn muffs be "c"; bran muffs be "b":
Milk Inequality: 4c + 2b <= 16
Flour Inequlity: 3c + 3b <= 15
-------------
Solve each inequality for "c":
Milk: c <- (-1/2)b + 4
Flour:c <= -b + 5
---------------------------------------
Graph these inequalities:

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.
--------------------------------------------
He makes $3 profit per tray of corn muffins and $2 profit
per tray of bran muffins.
----------------------------------------------
Object function = 2b + 3c represents the total profit for
each combination of b and c in the solution set.
----------------
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
---------------------------------------------
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
======================
Cheers,
Stan H.
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