Question

Question 4 Suppose that the price-Demand (p-D) relationship for a product is p Cost (TC) of manufacturing the product is 10-0.2D and the Total TC 10-D+0.3D2 . (a) Determine the value of D that maximizes the Total Revenue, TR, and indicate how you know that this D maximizes TR. (10 marks) (b) Determine the value of D that maximizes profit, 11, and indicate how you know that this value of D maximizes Π. (10 marks)

Answer 1

Answer 4 a : P= 10-0.2D

PD= 10D -0.2D^{​​ 2}

^{​​​​​​}TR = 10D - 0.2 D^{​​​​​​ 2}

First derivative of total Revenue is and maximum shows that

10- 0.4D = 0

0.4D= 10

D= 25 units

With the help of taking first derivative we know that the value of D is equal to 25 units maximum revenue earned by firm.

When D= 25 units

TR= 10D - 0.2D ² = 10(25)- 0.2(25)²= 250-125= $125

When D= 30 units

TR = 10(30) - 0.2(30)² = $120

This shows that by selling more you need the total revenue has been decreased. It means that d is equal to 25 shows the maximum Total revenue the company generated.

b : Total profit (π ) = TR -TC

Total profit ( π . ) = 10D -0.2D ² -10+D -0.3D ²

Total profit = -0.5D² +11D -10

Derivative of the total profit maximum it's

-D +11=0

D= 11units

Therefore total profit is maximum where they sold D=11units

Total profit= $51

When D = 20unit

Total profit = -$69

This shows that D = 11units maximum the profit of the firm.