A producer of felt-tip pens has received a forecast of demand of 31,000 pens for the coming month from its marketing department. Fixed costs of $21,000 per month are allocated to the felt-tip operation, and variable costs are 25 cents per pen. a. Find the break-even quantity if pens sell for $1 each. (Round your answer to the next whole number.) QBEP units b. At what price must pens be sold to obtain a monthly profit of $18,000, assuming that estimated demand materializes

Explanation:

1. Break-even quantity

a) Revenue, R(x)

The  monthly revenue is the product of the price by the number of units sold in the month.

Naming x the number of pens sold in the month:

b) Cost, C(x)

The monthly cost is the sum of the fixed cost per month plus the variable costs:

c) Break-even

Break-even is the point when the revenue and the total costs are equal, this is, when the profit is zero. Write the equation and solve:

Hence, the break-even quantity is 28,000 pens.

2. Price pens must be sold to obtain a monthly profit of $18,000

Profit = Revenue - Total cost

Where p is the price.

Substitute the quantity demanded, x, with 31,000, and the profit, P(x) with 18,000:

Solve for p and compute:

That is $1.51 per pen.