Question 1011358: 6. A baker has 150, 90, and
150 units of ingredients A, B, and C, respectively. A loaf
of bread requires 1, 1, and 2 units of A, B, and C,
respectively. A cake requires 5, 2, and 1 units,
respectively. A pizza requires 3, 2, and 1 units,
respectively. The number of loaves of bread and pizzas
must each be at least three times the number of cakes.
If a loaf of bread sells for $0.75, a cake sells for $2, and
a pizza sells for $2.50, how many of each should he
bake to maximize his gross income?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A baker has 150, 90, and 150 units of ingredients A, B, and C, respectively.
A loaf of bread requires 1, 1, and 2 units of A, B, and C, respectively.
A cake requires 5, 2, and 1 units,respectively.
A pizza requires 3, 2, and 1 units,respectively.
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The number of loaves of bread and pizzas must each be at least three times the number of cakes.
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If a loaf of bread sells for $0.75, a cake sells for $2, and a pizza sells for $2.50, how many of each should he bake to maximize his gross income?
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A Equation:: b + 5c + 3p <= 150
B Equation:: b + 2c + 2p <= 90
C Equation:: 2b+ c + p <= 150
----
b = 3c
p = 3c
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Objective Function: Income = 0.75b + 2.00c + 2.50p
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Comment::
Substitute b = 3c and p = 3c into the A,B, and C inequalities to get:
3c + 5c + 9c <= 150
17c <= 150
c <= 150/17 = 8.82
----
11c <= 90
c <= 90/11 = 8.18
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10c <= 150
c <= 15
===
Conclusion:: c <= 8.18 ; b <= 24.55 ; p <= 24.55
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Maximum Income::
Income = 0.75b + 2.00c + 2.50p
Income = 0.75*24.55 + 2*8.18 + 2.5*24.55 = $96.15
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Cheers,
Stan H.
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