Advertisements
Advertisements
प्रश्न
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
उत्तर
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
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
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`
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 function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions
If the marginal revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x2
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
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
A company requires f(x) number of hours to produce 500 units. It is represented by f(x) = 1800x–0.4. Find out the number of hours required to produce additional 400 units. [(900)0.6 = 59.22, (500)0.6 = 41.63]
