Question 825911: A recipe calls for 2 ingredients and for no more than 15 grams of sugar or 16 grams of salt to be contained by the ingredients. One unit of ingredient A contains 1 gram of sugar, and 1 unit of ingredient B contains 3 grams of sugar. Also, 1 unit of ingredient A contains 4 grams of salt, and 1 unit of ingredient B contains 1 gram of salt. If the cost of 1 unit of ingredient A is $10.00 and the cost of 1 unit of ingredient B is $13.00, what is the maximum amount of money that could be spent on the 2 ingredients?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A recipe calls for 2 ingredients and for no more than 15 grams of sugar or 16 grams of salt to be contained by the ingredients.
One unit of ingredient A contains 1 gram of sugar,
and 1 unit of ingredient B contains 3 grams of sugar.
Also, 1 unit of ingredient A contains 4 grams of salt,
and 1 unit of ingredient B contains 1 gram of salt.
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Sugar Inequality: A + 3B <= 15
Salt Inequality::4A + B <= 16
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Modify:
A + 3B <= 15
12A+3B <= 48
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Subtract to get:
11A <=33
A <= 3 (# of ingrediant A's needed)
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To solve for "B":
4A + 12B <= 60
4A + B <= 16
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Subtract and solve for "B":
11B <= 44
B <= 4 (# of ingrediant B's needed)
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If the cost of 1 unit of ingredient A is $10.00 and the cost of 1 unit of ingredient B is $13.00, what is the maximum amount of money that could be spent on the 2 ingredients?
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Ans: Max cost for 3A's and 4B's = 3*10 + 4*13 = 30+52 = $82.00
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Cheers,
Stan H.
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