Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
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 cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = x2 + 2x – 1
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/-.
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
Differentiate the following w.r.t.x :
y = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
Differentiate the following w.r.t.x :
y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
