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 monthly production that will maximize the total revenue and calculate the corresponding total profit per month. Determine also the corresponding average production cost per thousand board feet of plywood at this level of production.

Answer 1

p = $600 - 0.05D with maximum price (a) = $600 and reduction per thousand of board feet ie. standard deviation (b) = $0.05

Variable cost (c) = $155 per thousand board

Fixed cost per month = $800000

The optimum demand defined by D = maximum price - variable cost / 2 * Standard Deviation

= 600 - 155 / 2 * (0.05) = 4450 units (ie. 1000 boards)

Price = 600 - 0.05 * 4450 = $377.50 per unit

Maximum total revenue = 4450 * $377.50 = $1679875

Total profit = total revenue - total costs

= total revenue - total variable costs - total fixed costs

= $1679875 - ($155 * 4450) - 800000

= $190125

The corresponding average production cost per thousand board feet =

= (total variable costs + total fixed costs) / Total units production

= [($155 * 4450) + 800000] / 4450

= ($689750 + 800000) / 4450

= $1489750 / 4450 = $334.78