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
Elasticity of a function `("E"y)/("E"x)` is given by `("E"y)/("E"x) = (-7x)/((1 - 2x)(2 + 3x))`. Find the function when x = 2, y = `3/8`
The elasticity of demand with respect to price for a commodity is given by `((4 - x))/x`, where p is the price when demand is x. Find the demand function when the price is 4 and the demand is 2. Also, find the revenue function
A company receives a shipment of 500 scooters every 30 days. From experience, it is known that the inventory on hand is related to the number of days x. Since the shipment, I(x) = 500 – 0.03x2, the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days
The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is ₹ 120. Find the profit function
If MR = 20 – 5x + 3x2, Find total revenue function
Choose the correct alternative:
The marginal revenue and marginal cost functions of a company are MR = 30 – 6x and MC = – 24 + 3x where x is the product, then the profit function is
Choose the correct alternative:
The demand function for the marginal function MR = 100 – 9x2 is
Choose the correct alternative:
When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 – x2 is
A manufacture’s marginal revenue function is given by MR = 275 – x – 0.3x2. Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units
The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.
