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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)

Respuesta :

bhuvna789456
  • The break-even quantity if pens sell for $3 each = $ 12595.
  • The price at which the pens to be sold to obtain a monthly profit of $14,000 is $ 1.58

Explanation:

Given,   demand = 39000 pens, Fixed cost = $ 33000,

variable cost = 38 percent per pen = $ 0.38

  • The break even quantity is calculated using the formula,

Break even point = Fixed cost / (price per unit - variable cost per unit)

                              = 33000 / (3 - 0.38)

Break even point  = $ 12595.

  • So the monthly cost to make 39000 pens is going to be

               Fixed cost + demand [tex]\times[/tex] variable cost

                  33,000 + 39,000 [tex]\times[/tex] 0.38 = $ 47820.

      But, we want to make $ 14,000 more than that so let's add it together   to get the amount we need to make.

                      47820 + 14,000 = $ 61820.

     so we're selling 39,000 pens and we need to get $ 61820 out of them so 61820 is divided by 39,000.

                      61820 / 39000 = $ 1.58.