Question 85175: I need help....
Income A baker has 150 units of flour, 90 of sugar, and
150 of raisins. A loaf of raisin bread requires 1 unit of flour,
1 of sugar, and 2 of raisins, while a raisin cake needs 5, 2,
and 1 units, respectively.
a. If raisin bread sells for $1.75 a loaf and raisin cake for
$4.00 each, how many of each should be baked so that
gross income is maximized?
b. What is the maximum gross income?
c. Does it require all of the available units of flour, sugar,
and raisins to produce the number of loaves of raisin
bread and raisin cakes that produce the maximum profit?
If not, how much of each ingredient is left over?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Income A baker has 150 units of flour, 90 of sugar, and
150 of raisins. A loaf of raisin bread requires 1 unit of flour,
1 of sugar, and 2 of raisins, while a raisin cake needs 5, 2,
and 1 units, respectively.
:
Graphing will be useful here.
:
Let x = no. of loaves of raisin bread
Let y = no. of raisin cakes
:
Flour equation:
1x + 5y = 150
5y = 150 - x
y = 30 - .2x; green
:
Sugar equation
1x + 2y = 90
2y = 90 - x
y = 45 - .5x; purple
:
Raisin equation
2x + y = 150
y = 150 - 2x; black
:
:
a. If raisin bread sells for $1.75 a loaf and raisin cake for
$4.00 each, how many of each should be baked so that
gross income is maximized?
:
Look at the corners of the area of feasibility, we have
x = 0, y = 30
x = 50, y = 20
x = 70, y = 10
x = 75, y = 0
:
b. What is the maximum gross income?
:
Using these value for x and y, find the income for each kind.
x = 50, y = 20 would have the greatest income:
(1.75*50) + (4 * 20) = $167.50
:
c. Does it require all of the available units of flour, sugar,
and raisins to produce the number of loaves of raisin
bread and raisin cakes that produce the maximum profit?
:
No
:
If not, how much of each ingredient is left over?
:
Flour equation:
1(50) + 5(20) = 150, used all the flour
Sugar equation:
1(50) + 2(20) = 90, used all the sugar
Raisin equation
2(50) + 1(20) = 140, 150 - 120 = 30 units of raisins left over
:
I think the method is valid, but check my math here.
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