Advertisements
Advertisements
Question
If the marginal cost function of x units of output is `"a"/sqrt("a"x + "b")` and if the cost of output is zero. Find the total cost as a function of x
Advertisements
Solution
M.C = `"a"/sqrt("a"x + "b")`
Total cost function
C = `int ("M.C") "d"x`
C = `int "a"("a"x + "b")^(1/2) "d"x`
= `int "a"("a"x + "b")^((-1)/2) "d"x + "k"`
= `"a"[(("a"x + "b")^((-1)/2) + 1)/(((-1)/2 + 1) xx ("a"))] + "k"`
C = `[("a"x + "b")^(1/2)/((1/2))] + "k"`
∴ C(x) = `2("a"x + "b")^(1/2)` ........(1)
When x = 0
Equation (1)
⇒ 0 = `2["a"(0) + "b"]^(1/2) + "k"`
k = `-2("b")^(1/2)`
⇒ k = `-2sqrt("b")`
Required cost function
C(x) = `2("a"x + "b")^(1/2) - 2sqrt("b")`
∴ C = `2sqrt("a"x + "b") - 2sqrt("b")`
APPEARS IN
RELATED QUESTIONS
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
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
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
Given the marginal revenue function `4/(2x + 3)^2 - 1` show that the average revenue function is P = `4/(6x + 9) - 1`
The demand function for a commodity is p =`36/(x + 4)`. Find the consumer’s surplus when the prevailing market price is ₹ 6
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 MR = 35 + 7x – 3x2, then the average revenue AR is
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
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
