Question

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

To find the maximum quantity the firm should produce to break even, set total revenue equal to total cost and solve for the quantity using the given price and costs. The maximum quantity is 3 units.

Step-by-step explanation:

To determine the maximum quantity the firm should produce to break even, we need to find the breakeven point where the total revenue equals the total cost. The total revenue is the product of the quantity sold and the price, which is given by TR = p*q. The total cost is the sum of fixed cost and variable cost, which is given by TC = FC + VC*q. To find the breakeven point, we set TR equal to TC and solve for the quantity, as follows:

p*q = FC + VC*q

200 - 5q*q = 100 + 10q*q

Expanding the equation, we get:

200 - 5q^2 = 100 + 10q^2

15q^2 = 100

q^2 = 100/15

q = √(100/15)

Using a calculator, we get q ≈ 3.055. Since we cannot produce a fractional quantity, we round down to the nearest whole number. Therefore, the maximum quantity the firm should produce to break even is 3 units.