Question 1: The cost function of a manufacturing concern is linear as follows:

C(x) = 25x + 15,000 where C(x) is the total cost in dollars of producing x units, x is the number of units produced .

Its revenue function is non-linear, however, as follows:

R(x) = -0.01x² + 50x R(x) is the total revenue in dollars from the sale of x units x is the number of units sold

a) What is the profit function?

b) Find the breakeven points for this firm.

c) What would be the maximum profit, and how many units of their product must be sold to achieve this maximum?

Question 2: The profit made by a company that produces and sells x units of an appliance is given by P(x) = 300x - 25x² 

a) Determine the breakeven level of production.

b) What level of production is necessary to maximize profit?

c) What is the maximum profit?