Advertisements
Advertisements
प्रश्न
Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x2
उत्तर
The marginal revenue function
MR = 10 + 3x – x2
The Revenue function
R = `int ("MR") "d"x`
= `int (10 + 3x - x^2) "d"x`
R = `[10x + 3(x^2/2) - (x^3/3)] + "k"`
When x = 0
R = 0
⇒ k = 0
∴ R = `10x + (3x^2)/2 - x^3/3`
⇒ px = `10x + (3x^2)/2 - x^3/3`
⇒ p = `(10x + (3x^2)/2 - x^3/3)/x`
∴∴ The demand function p = `10 + (3x^2)/2 - x^2/3`
APPEARS IN
संबंधित प्रश्न
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`
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
The demand and supply functions under perfect competition are pd = 1600 – x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus
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:
The profit of a function p(x) is maximum when
Choose the correct alternative:
The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 is
The marginal cost of production of a firm is given by C'(x) = `20 + x/20` the marginal revenue is given by R’(x) = 30 and the fixed cost is ₹ 100. Find the profit function
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.
