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?
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b >= 0
p >= 0
Comment:: The above inequalities mean you are only interested
in the 1st Quadrant for alswers.
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Flour Inequality:: 2b + 3p <= 30 cups
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Sugar Inequality:: b + 2p <= 16 cups
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Objective Function::
Profit = 2.5b + 4p
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Rearrange inequalities::
Flour:: b <= (-3/2)p + 15
Graph the boundary and shade the half-plane below the boundary.
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Sugar:: b <= -2p+16
Graph the boundary and shade the half-plane below the boundary
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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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