Question

The Extraordinary Manufacturing Company has established that the relationship between sales price for one of its products and the quantity sold per month is approximately 3D=1680-39p units. The fixed cost is P1500 per month, the variable cost is P45 per unit produced.

• What number of units should be produced and sold per month to maximize net profit? What is the maximum profit?
• What is the production range of profitable business for the company?

Answer 1

Given

$3D=1680-3P$

Fixed cost=1500

Variable cost=45

Rearrange

$3D=1680-3D\\3P=1680-3D\\P=560-D$

a)

Profit maximizing level

$MR=MC\\TR=P×D\\TR=(560-D)D^2\\MR=\frac{dTR}{dD}=560-2D\\TC=1500+45D\\MC=\frac{dTC}{dD}=45$

Now MR=MC

$560-2D=45\\560-45=2D\\D=257.5\\P=560-D\\P=560-257.5=302.5$

Profit=TR-TC

$TR=560D-D^2\\=560(257.5)-(257.5×257.5)\\=144200-66306.25\\=77893.75$

$TC=1500+45D\\=1500+45(257.5)\\=1500+11.587.5\\=13087.5$

Profit$=77893.75-13087.5=64806.25$

b)

$Range=257.5-0.5=257\\257+0.5=258\\257-258$