SOLUTION: A bakery owner wants to make a profit of at least twice the price it costs to produce each item. It costs between 30 and 40 cents to produce a loaf of date bread. What is the least

Question 1161904: A bakery owner wants to make a profit of at least twice the price it costs to produce each item. It costs between 30 and 40 cents to produce a loaf of date bread. What is the least amount he can charge for each loaf of date bread?
Found 2 solutions by greenestamps, Theo:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

If he wants the profit to be at least twice the cost of production, then the selling price needs to be at least three times the cost of production.

To ensure that level of profit, you need to assume the upper end of the range of the cost of production.

So the minimum cost to assure a profit of twice the cost of production is three times 40 cents, or $1.20.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
in order to have a profit of at least twice the cost, then the sale price must be at least 3 times the cost price.

the general formula would be:

p = (s - c) / c

p is the profit.
s is the sale price
c is the cost price

simplify this equation to get:

p = s/c - c/c

this makes p = s/c - 1.

that means the profit is equal to the sale price divided by the cost price minus 1.

this means that, if you want a profit of at least twice the cost price, you need a sale price at least 3 times the cost price.

for example:

if the cost price is 1 dollar, then the sale price has to be at least 3 dollars, because the profit would then be 2 dollars which is 2 times the cost price.

therefore, if the cost was .30 then the sale price would have to be at least .90, and if the cost was .40 then the sale price would have to be at least 1.20.

since the cost per loaf is variable, then, if possible (competition challenges might indicate otherwise), the highest cost should be assumed.

this means that the minimum sale price should be 1.20.

based on a sale price of 1.20:

if the cost price was .30, then the sale price would be 1.20 /.30 = 4 times the cost price and the profit would be (1.20 - .30) / .30 = 3 times the cost price.

if the cost price was .40, then the sale price would be 1.20 / .40 = 3 times the cost price and the profit would be (1.20 - .40) / .40 = 2 times the cost price.

in both cases, the sale price would be at least 3 times the cost price and the profit would be at least 2 times the cost price.

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