Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
M.C αx
M.C = λx
fixed cost k = ₹ 5000
Cost function C = `int ("M.C") "d"x`
= `int lambdax "d"x`
C = `(lambdax^2)/2 + "k"`
⇒ C = `lambda (x^2/2) + 5000` ........(1)
When x = 50 then C = 5625
5625 = `(lambda(50)^2)/2 + 5000`
5625 – 5000 = `(lambda(2500))/2 = 1250 lambda`
`1250 lambda = 625`
⇒ `lambda = 625/1250 = 1/2`
∴ Required total cost function from equation (1)
C = `1/2(x^2/2) + 5000`
∴ C = `x^2/4 + 5000`
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)
The marginal cost function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions
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)
If the marginal revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
The demand function p = 85 – 5x and supply function p = 3x – 35. Calculate the equilibrium price and quantity demanded. Also, calculate consumer’s surplus
The demand function for a commodity is p = e–x .Find the consumer’s surplus when p = 0.5
The demand function for a commodity is p =`36/(x + 4)`. Find the consumer’s surplus when the prevailing market price is ₹ 6
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 and supply function of a commodity are P(x) = (x – 5)2 and S(x) = x2 + x + 3 then the equilibrium quantity x0 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
