Question 80433
a batch of raisin cakes requires 5 lbs. of flour, 2 lbs. of sugar, and 1 lb. of raisins.
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A batch of raisin pies requires 2 lbs. of flour, 3 lbs. of sugar and 4 lbs of raisins.
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Let x = no. of batches of cakes, y = no. of batches of pies
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there are 165 lbs. of flour, 110 lbs. of sugar and 120 lbs. of raisins available each week.
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Write an equation for each ingredient, put in the form for graphing:
Flour: 5x + 2y =< 165
2y = 165 - 5x
y = 82.5 - 2.5x; 
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Sugar: 2x + 3y =< 110
3y = 110 - 2x
y = 36.67 - .67x
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Raisins: x + 4y =<120
y = 30 - .25x
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Standing orders require at least five batches of raisin cakes and eight batches of raisin pies per week.
y => 8
x => 5
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Graph all the above, you have to add the vertical line at x = 5
{{{ graph( 300, 200, -10, 40, -10, 40, 82.5-2.5x, 36.67 - .67x, 30-.25x, 8) }}} 
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The corners of the feasibility region, rounded down if a fraction are
x | y
------
5 | 8
5 | 28
15| 26
25| 19
28| 8
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If profit on a batch of raisin cakes is $35 and profit on a batch of raisin pies is $40, how many batches of each should be made per week to maximize profit?
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35x + 40y = $profit
Substitute x & y from the above table
35(5) + 40(8) = $495
35(5) + 40(28) = $1295
35(15) + 40(26) =$1565
35(25) + 40(19) =$1635
35(28)  + 40(8) = $1300
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You can see which Combination of cakes & pies are the most profitable, however
 check each step here, there is much chance for error, I have confidence in the
 method, but my math is often not so good

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