Question

A group of students bakes 100 cookies to sell at the school bake sale. The students want to ensure that the price of each cookie offsets the cost of the ingredients. If all the cookies are sold for $0.10 each, the net result will be a loss of $4. If all the cookies are sold for $0.50 each. The students will make a $36 profit. First, write the linear function p(x) that represents the net profit from selling all the cookies, where x is the price of each cookie. Then, determine how much profit the students will make if they sell the cookies for $0.60 each. Explain. Tell how your answer is reasonable.

Answer 1

46

Explanation:

-Let b be the constant in the linear equation.

#The linear equation can be expressed as:

`p(x)=100x+b`

Substitute the values in the equation to find b:

`p(x)=100x+b\\\\-4=100(0.1)+b\\\\b=-14\\\\\#or\\\\36=100(0.5)+b\\\\b=-14`

We know have the constant value b=-14, substitute the values of b and x in the p(x) function:

`p(x)=100x+b\\\\p(x)=100(0.6)-14\\\\p(x)=60-14\\\\p(x)=46`

Hence, the profit when selling price is $0.60 is $46

#From our calculations, it's evident that the cookies production has a very high fixed cost which can only be offset by raisng the selling price or the number of units sold at any given time.