Question

Problems 1-6 are based on the following information: A company sells PC software whose price is determined by p = 200 - 5Q, where Q is the quantity purchased per day. It has fixed costs of $100 per day and variable costs of $10 per unit sold.

The maximum quantity the firm should produce to breakeven is __________.

	A.	30
	B.	25
	C.	48
	D.	38
	E.	32

Answer 1

Condition for break even point of sale is :-

Total Revenue (TR) = Total Cost (TC)

As, TR = P * Q = (200-5Q) * Q = 200Q - 5Q2

Now, TC = Fixed Cost + Total Variable Cost

TC = Fixed Cost + (Variable cost per unit * Q)

So, TC = 100 + 10Q

Now,Using Breakeven point condition

200Q - 5Q2 = 100 + 10Q

5Q2 -200Q + 10Q + 100 = 0

5Q2 - 190Q +100 = 0

Using Quadratic equation formula of finding roots:-

Since quantity can't be in decimals so the breakeven quantity will be rounded up.

So, Q = 38

The maximum quantity firm must produce to break even is 38

• Hence, Option D. 38 is correct