A producer of felt-tip pens has received a forecast of demand of 39,000 pens for the coming month from its marketing department. Fixed costs of $33,000 per month are allocated to the felt-tip operation, and variable costs are 38 cents per pen.

a. Find the break-even quantity if pens sell for $3 each. (Round your answer to the next whole number.)

b. At what price must pens be sold to obtain a monthly profit of $14,000, assuming that estimated demand materializes? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

(a) 12,595.4 units

(b) $1.59

Explanation:

Demand = 39,000

Fixed cost = $33,000 per month

Variable costs = 38 cents per pen

(a) Revenue per unit = $3

Let the volume be x,

Total cost:

= Fixed cost + Variable cost

= $33,000 + (0.38x)

Total revenue = Revenue per unit * Volume

= 3x

TR = TC

3x = $33,000 + (0.38x)

3x - 0.38x = $33,000

2.62x = $33,000

x = 12,595.4 units

(b) Let the revenue per unit be x,

Total cost:

= Fixed cost + Variable cost

= $33,000 + (0.38 * 12,595)

= $47,820

Total revenue = Revenue per unit * Volume

= 39,000x

Profit = Total revenue - Total cost

$14,000 = 39,000x - $47,820

39,000x = 61,820

x = 1.5851 or $1.59