Advertisements
Advertisements
Question
Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n2 + `"n"^3/5`. Find the marginal cost at n = 10.
Advertisements
Solution
Total cost function,
C = 1500 − 75n + 2n2 + `"n"^3/5`
Marginal Cost = `("dC")/("dn")`
=`"d"/("dn")(1500 - 75"n" + 2"n"^2 + "n"^3/5)`
=`d/(dn)(1500) - 75"d"/("dn")("n")+2"d"/("dn")("n"^2) + 1/5"d"/("dn")("n"^3)`
= `0 - 75(1) + 2(2"n")+1/5(3"n"^2)`
= `-75 + 4"n" + (3"n"^2)/5`
When n = 10,
Marginal cost
=`(("dC")/("dn"))_("n" = 10)`
= `-75 + 4(10) + 3/5 (10)^2`
= –75 + 40 + 60
= 25
∴ Marginal cost at n = 10 is 25.
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.
Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
Solve the following example: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx` if y = (1 – x) (2 – x)
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
The supply S of electric bulbs at price P is given by S = 2P3 + 5. Find the marginal supply when the price is ₹ 5/- Interpret the result.
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
