Question

Question 2.(10 points): The cost (in thousands of dollars) for building a new apartment was estimated to be C(x) -1,575 + 185x for 10 s x s 150 (where x is the number of apartments). Suppose that the owning company is selling its apartments at the price of $220,000 (for each apartment). Find the revenue function of this company? Find its profit function? How many apartments does it sell to break even? Can the company make profit?

Answer 1

Revenue function :

R(x) = price * number of apartments

= 220,000*x

Now profit function:

π(x) = total revenue - total cost

= R(x) - C( x)

= 220,000*x -1575 - 185*x

π (x) = 219,815*x - 1575

Now at break even case, total revenue becomes equal to total cost.

So π(x) = 0

So x = 1575/ 219,815

= 0.007 thus zero apartment

Thus company always make profit if it sells the apartments.