Question

A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $50. The fixed cost that can be allocated to the production of fireworks is negligible. The price charged per unit will be determined by the equation p = $200 − 5D, where D represents demand in units sold per week.

a) What is the optimum number of units the defense contractor should produce in order to maximize profit per week?

b) What is the profit if the optimum number of units are produced?

c) What is the range of profitable demand during a week?

d) Is it worthwhile to produce 30 units per week? Why?

Answer 1

Fixed Cost= 0

Variable cost = $50

Inverse Demand Funtion => P= $200-5D Therefore, a= 200, b=5

(a)

= 15 units are optimum

(b) Profit = Total revenue - Total cost

= (200-5D)D - (50*D)

Since, D= 15

therefore Profit= (200D-5D^2) - 50D

P= (200*15 - 5(15)^2) -50*15

P= (3000-1125) - 750

P = 1875-750 = 1125

P=$1125 When optimum number of units are produced.

(c) The range of profitable demand during a week will be

1 unit to 29 units

(d) On producing 30 units a week

Profit = Total revenue - Total cost

= (200-5D)D - (50*D)

D= 30

therefore Profit= (200D-5D^2) - 50D

P= (200*30 - 5(30)^2) -50*30

P= (6000-4500) - 1500

P = 1500-1500 = 0

P=$ 0, Therefore, it will not be profitable if 30 units are produced in a week.