Question

A factory manager is planning for the manufacture of plywood to be sold overseas. The fixed cost of operation is estimated at​ $800,000 per month while the variable cost is​ $155 per thousand board feet of plywood. The selling price will depend on how much will be produced and sold and is determined by the​ relationship, price per thousand board​ feet, p​ = $600​ – 0.05D, where D is the amount produced and sold in thousands of board feet. Determine the range of profitable production. For profitable​ production, production must be at least (blank) thousands of board feet per​ month, but not more than (blank).

Answer 1

Solutions:

Fixed cost=$800,000

VC=​ $155 / thousand board feet of plywood

p​ = $600​ – 0.05D   (D is the amount produced and sold in thousands of board feet)

Range of profitable production

Profit Range: It refers to the range of prices, which return a profit for a business.

Here, TC=TFC+VC

Total Revenue= Price X Quantity

            ($600​ – 0.05D)   X D (where D is the Quantity)

=$600D​ – 0.05D²

MR=dTR/dD

=$600-0.10D

TC= TFC+TVC

=$800000+$155D (Where D is the Quantity)

MC=dTC/dD =$155

The profitable range of production occurs when MR=MC

We have MR=$600-0.10D

MC=$155

MR=MC

=$600-0.10D=$155

=$600-$155=0.10D

= D=4450

P=$600​ – 0.05D   =$600​ – 0.05(4450)   =$600-222.50=337.50

Therefore, the profitable range of production would be to producing 4450 units of production at price $337.50 per thousand board feet.