Answer to Question #224874 in Economics of Enterprise for chhhin

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)

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