Expert: Richard J. Raridon - 11/20/2011

Question
I am 60 years old,and I need help with this algebra problem.

Your company has asked you to research the smartphone competitive market. Through research, you have modeled the industry data and found that the cost (in thousands of dollars) of producing a certain number of smartphones can be given by the following polynomial:


Expenses = x2 + 800

where x = the number of smartphones in thousands.

The revenue (also in thousands of dollars) generated in selling the same amount is given by the expression 100x. That is,

Revenue = 100x

Use the following knowledge to determine the profit by subtracting the expenses from the revenue:

a.Give a polynomial expression that can be used to compute the profit. Briefly explain how this was done.
b.Use the expression you just derived to compute the profit if 50,000 smartphones are sold. (Note: Remember that the profit is expressed in thousands of dollars, so a computed value of, say, 30 means $30,000.). Show the steps of the computation. After making the computation, interpret the results in real-life terms.

Answer
a. profit = 100x-x^2-800
b. if x =50, profit = 1700 or $1,700,000
That also turns out to be the maximum profit.  
That's a strange expense function since you would think the cost per unit would decrease if you made more.  I'm 80 years old and glad to help you.