SOLUTION: You have 140 tomatoes and 13 onions left over from your garden. You want to use these to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato sauce

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You have 140 tomatoes and 13 onions left over from your garden. You want to use these to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato sauce       Log On


   

Question 1054281: You have 140 tomatoes and 13 onions left over from your garden. You want to use these to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato sauce requires 10 tomatoes and 1 onion, and a jar of salsa requires 5 tomatoes and 1/4 onion. You will make a profit of $2 on every jar of tomato sauce sold and a profit of $1.50 on every jar of salsa sold. The owner of the farm stand wants at least three times as many jars of tomato sauce as jars of salsa. How man jars of each should you make to maximize profit?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let X be the jars of sauce, Y be the jars of salsa,
Look at how many tomatoes are used,
10X%2B5Y%3C=140
Look at how many onions are used,
X%2BY%2F4%3C=13
Finally identify the profit,
P=2X%2B1.5Y
Graphing the feasible region,
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.
.
.
.
.
.
Check the profit at each of the vertices,
(0,28):P=2%280%29%2B1.5%2828%29=42
(12,4):P=2%2812%29%2B1.5%284%29=30
(13,0):P=2%2813%29%2B1.5%280%29=26
The most profit is made by only making salsa.
28 jars getting you $42.
However the farm stand owner wants 3X jars of sauce versus salsa so (12,4) would yield $30 profit.
You may want to convince her that she's losing $12 profit and change her view.