SOLUTION: "A company calculates it's profit by finding the difference between revenue and cost. The cost function of producing x hammers is C(x) = 4x+170. If each hammer is sold for $10, t

Algebra ->  Functions -> SOLUTION: "A company calculates it's profit by finding the difference between revenue and cost. The cost function of producing x hammers is C(x) = 4x+170. If each hammer is sold for $10, t      Log On


   

Question 138710: "A company calculates it's profit by finding the difference between
revenue and cost. The cost function of producing x hammers is C(x) =
4x+170. If each hammer is sold for $10, the revenue function for
selling x hammers is R (x) = 10x."

1.) How many hammers must be sold to make a profit?

2.) How many hammers must be sold to make a profit of $100?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1)


The profit function is defined by:

Profit = Revenue - Cost



So in function notation it looks like:

P%28x%29=R%28x%29-C%28x%29


So in our case:

P%28x%29=10x-%284x%2B170%29 Plug in R%28x%29=10x and C%28x%29=4x%2B170


P%28x%29=10x-4x-170 Distribute the negative


P%28x%29=6x-170 Combine like terms


6x-170%3E0 Set the right side greater than zero. Remember we're looking for positive profit.


6x%3E170 Add 170 to both sides


x%3E170%2F6 Divide both sides by 6


x%3E28.333 Divide


x%3E29 Round to the nearest whole number. A third of a hammer can't be sold.



So when x%3E29, we'll have positive profit. So more than 29 hammers must be sold to gain a profit.






2)

We're still using the profit function. So P%28x%29=6x-170


Since we want a profit of $100, simply plug in P%28x%29=100.


P%28x%29=6x-170 Start with the profit function


100=6x-170 Plug in P%28x%29=100


270=6x Add 170 to both sides


45=x Divide both sides by 6


So when x=45, we'll have a profit of $100. So 45 must be sold to make a profit of $100.