A company’s revenue, R, is given by the function = 300 − 22 where x is the number of items sold. The company’s cost for x items, C, is given by the function = 5000 + 40. The profit of the company, P, can be found by subtracting its cost from its revenue. = − .
a) Create a simplified expression for the profit function. Remember to use brackets when you subtract the cost function from the revenue function since the minus sign will change the sign of all of the terms in the cost function. = (300 − 22) − (5000 + 40). The simplified profit function will be quadratic. Make sure it is in the form = 2 + +
b) Realistically, what are all the possible values that x could be? Consider what the variable x represents when answering this question.
c) How much money does the company lose if it doesn’t sell any items? d) How much does the company profit if it sells 35 items?
e) Tell me at least 2 ways you could find the maximum profit algebraically, then find the maximum profit of the company algebraically using a method of your choice. Show all of your work!