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`
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
The marginal cost function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions
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
Calculate consumer’s surplus if the demand function p = 50 – 2x and x = 20
The demand equation for a products is x = `sqrt(100 - "p")` and the supply equation is x = `"P"/2 - 10`. Determine the consumer’s surplus and producer’s surplus, under market equilibrium
Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x
Choose the correct alternative:
If the marginal revenue function of a firm is MR = `"e"^((-x)/10)`, then revenue is
Choose the correct alternative:
The demand and supply functions are given by D(x) = 16 – x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is
Choose the correct alternative:
The demand function for the marginal function MR = 100 – 9x2 is
Choose the correct alternative:
If the marginal revenue of a firm is constant, then the demand function is
