Kanesha is making scented candles to sell at the craft fair. She buys a 5-pound package of candle wax, a package of 12 small candle tins that each have a volume of 4 ounces and the package of 12 medium candle tins that each have a volume of 6 oz. Kanesha knows that 1 lb of candle wax will fill 20 oz in volume.
Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...
____ small 4 oz candles
____ medium 6 oz candles
what is the maximum amount of money she will earn in the craft fair?
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1 lb of candle wax will fill 20 oz
She buys a 5-pound package, therefore, she will fill 20*5= 100 oz
Tin size S small (4 oz ) and M medium (6 oz)
S*4 + M*6 = 100
S*7.5 + M*9 = amount of money
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S*4 + M*6 = 100
4 S = 100 - 6M
S= 100/4 -6/4M
S= 25 -3/2M
Replacing
(25 -3/2M )*7.5 + M*9 = amount of money
187.5 - 11.25M + 9M = amount of money
187.5 - 2.25M = amount of money
According to the expression, the fewer medians sell, the higher the income will be.
Reviewing the candle values by ounces used.
7.5/ 4 = 1.875 sale price / oz
9.0/6 = 1.5 sale price / oz
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Therefore, in order to maximize the profit, it would be necessary to make as many small ones as possible, that is, 12.
12* 4 oz = 48
100- 48 = 52
what is left after using the 4 oz tins can be used in the medium candles
52/ 6 = 8
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Answer
Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...
__12__ small 4 oz candles
___8_ medium 6 oz candles