Advertisements
Advertisements
प्रश्न
Given the marginal revenue function `4/(2x + 3)^2 - 1` show that the average revenue function is P = `4/(6x + 9) - 1`
Advertisements
उत्तर
M.R = `4/(2x + 3)^2 - 1`
Total Revenue R =`int"M.R" "d"x`
R = `int (4/(2x + 3)^2 - 1) "d"x`
= `int [4(2x + 3)^-2 - 1] "d"x`
R = `[4[(2x + 3)^(-2 + 1)/(-2 + 1)] - x] + "k"`
R = `4[(2x + 3)^1/((-1) xx 2)] - x + "k"`
R = `4[1/(-2(2x + 3))] - x + "k"`
R = `(-2)/((2x + 3)) - x + "k"` .......(1)
When x = 0
R = 0
⇒ 0 = `(-2)/([2(0) + 3]) - 0 + "k"`
0 = `(-2)/3 + "k"``
⇒ k = `2/3`
From eqaution (1)
⇒ R = `(-2)/((2x + 3)) - x + 2/3`
⇒ R = `2/3 - 2/((2x + 3)) - x`
R = `(2(2x + 3) - 2(3))/(3(2x + 3)) - x`
= `(4x + 6 - 6)/((6x + 9)) - x`
∴ R = `(4x)/((6x + 9)) - x`
Average Revenue A.R = `"R"/x`
= `([(4x)/((6x + 9)) x])/x`
A.R = `4/((6x + 9)) - 1`
APPEARS IN
संबंधित प्रश्न
The cost of an overhaul of an engine is ₹ 10,000 The operating cost per hour is at the rate of 2x – 240 where the engine has run x km. Find out the total cost if the engine runs for 300 hours after overhaul
An account fetches interest at the rate of 5% per annum compounded continuously. An individual deposits ₹ 1,000 each year in his account. How much will be in the account after 5 years. (e0.25 = 1.284)
Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C'(x) = `x^2/200 + 4`
The marginal revenue (in thousands of Rupees) functions for a particular commodity is `5 + 3"e"^(- 003x)` where x denotes the number of units sold. Determine the total revenue from the sale of 100 units. (Given e–3 = 0.05 approximately)
A firm’s marginal revenue function is MR = `20"e"^((-x)/10) (1 - x/10)`. Find the corresponding demand function
If the marginal cost (MC) of production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000 and the cost of producing 50 units is ₹ 5,625
Choose the correct alternative:
If the marginal revenue function of a firm is MR = `"e"^((-x)/10)`, then revenue is
Choose the correct alternative:
For the demand function p(x), the elasticity of demand with respect to price is unity then
Choose the correct alternative:
When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 – x2 is
Choose the correct alternative:
When x0 = 2 and P0 = 12 the producer’s surplus for the supply function Ps = 2x2 + 4 is
