SOLUTION: Baking a loaf of banana bread takes 2 cups of flour and 1 cup of sugar. A loaf of pumpkin bread takes 3 cups of flour and 2 cups of sugar. A baker has 30 cups of flour and 16 cups

Question 955582: Baking a loaf of banana bread takes 2 cups of flour and 1 cup of sugar. A loaf of pumpkin bread takes 3 cups of flour and 2 cups of sugar. A baker has 30 cups of flour and 16 cups of sugar to use. She makes $2.50 profit per loaf of banana bread and $4.00 profit per loaf of pumpkin bread. How many loaves of each type of bread should the baker make to maximize her profit?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Baking a loaf of banana bread takes 2 cups of flour and 1 cup of sugar.
A loaf of pumpkin bread takes 3 cups of flour and 2 cups of sugar.
A baker has 30 cups of flour and 16 cups of sugar to use.
She makes $2.50 profit per loaf of banana bread and $4.00 profit per loaf of pumpkin bread.
How many loaves of each type of bread should the baker make to maximize her profit?
-------------------
b >= 0
p >= 0
Comment:: The above inequalities mean you are only interested
in the 1st Quadrant for alswers.
-----------------
Flour Inequality:: 2b + 3p <= 30 cups
-----
Sugar Inequality:: b + 2p <= 16 cups
------
Objective Function::
Profit = 2.5b + 4p
====================
Rearrange inequalities::
Flour:: b <= (-3/2)p + 15
Graph the boundary and shade the half-plane below the boundary.
----------------------------------
Sugar:: b <= -2p+16
Graph the boundary and shade the half-plane below the boundary
-----
Find the intersection of all of the boundaries.
Check each x/y pair in the objective function
to find the p/b pair that gives a maximum profit.
Cheers,
Stan H.

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