Question

A producer of felt-tip pens has received a forecast of demand of 30,000 pens for the coming month from its marketing department. Fixed costs of $25,000 per month are allocated to the felt-tip operation, and variable costs are 37 cents per pen.

a. Find the break-even quantity if pens sell for $1 each.

A) 16,216 pens
B) 40,541 pens
C) 67,568 pens
D) 135,135 pens

b. At what price must pens be sold to obtain a monthly profit of $15,000, assuming that estimated demand materializes?

A) $1.37 per pen
B) $1.48 per pen
C) $1.52 per pen
D) $1.63 per pen

Answer 1

The break-even quantity calculation and profit target selling price calculation for the felt-tip pens did not match any of the multiple-choice options provided; the correct break-even quantity is approximately 39,682 pens, and the correct selling price to achieve a $15,000 profit is $1.70 per pen.

Step-by-step explanation:

To find the break-even quantity of felt-tip pens, we set up the break-even point equation:

Break-even point in units = Fixed Costs / (Price per unit - Variable Cost per unit)

Fixed Costs = $25,000, Price per unit = $1, Variable Costs per unit = 37 cents.

Break-even point in units = $25,000 / ($1 - $0.37) = $25,000 / $0.63 = 39,682 pens (approximately)

Thus, none of the provided options A) 16,216 pens, B) 40,541 pens, C) 67,568 pens, or D) 135,135 pens are correct.

For part b, to sell pens at a price that achieves a profit of $15,000 when the forecasted demand is 30,000 pens, we can use the profit equation:

Profit = (Selling price per unit - Variable cost per unit) * Quantity sold - Fixed Costs

$15,000 = (Selling price per unit - $0.37) * 30,000 - $25,000

Selling price per unit = ($15,000 + $25,000 + ($0.37 * 30,000)) / 30,000

Selling price per unit = ($40,000 + $11,100) / 30,000

Selling price per unit = $51,100 / 30,000

Selling price per unit = $1.70 per pen

Therefore, again the options provided are not correct. The pens must be sold for $1.70 each to obtain a monthly profit of $15,000.