Answer to Question #212568 in Calculus for Akhona Klanisi

Question

Questions 11, 12  and  13  are  based  on  the  following  information: If a marginal revenue function of a rm is given as

MR = 10Q² + 6Q − 3,

 where Q is the number of units sold.

11

Find an expression for the total revenue function (TR).

1. ¹⁰/₃ Q³ + 3Q² - 3Q + C
2. ⁵/₃ Q³ + 6Q² - 3Q + C
3. Q³ + 3Q² - 3Q + C
4. ³/₅ Q³ + 3Q² - 3Q + C

12

Find the total revenue function if it is given that TR = 0 when Q = 0.

1. ¹⁰/₃ Q³ + 3Q² - 3Q
2. ⁵/₃ Q³ + 6Q² - 3Q + 1
3. Q³ + 3Q² - 3Q + 3
4. ³/₅ Q³ + 3Q² - 3Q

   13

Calculate the firm's total revenue when 5 units are sold.

[1      310,36

[2      200,00

[3      476,67

[4      532,67

Answer 1

Question 11

Integrating MR

$\int MR =\int( 10Q^2 + 6Q − 3)= TR$

$TR = \frac{10}{3}Q^3+3Q^2-3Q+C$

Option 1 is correct

Question 12

$TR = \frac{10}{3}Q^3+3Q^2-3Q+C$

$0= \frac{10}{3}*0^3+3*0^2-3*0+C \implies C=0$

$TR = \frac{10}{3}Q^3+3Q^2-3Q$

Option 1 is correct

Question 13

$TR = \frac{10}{3}Q^3+3Q^2-3Q$

$TR = \frac{10}{3}*5^3+3*5^2-3*5$

$TR = 476.66$

Option 3 is correct