A manufacturer-s marginal cost function is 500-2x-25- Find the cost involved to increase production from 100 units to 300 units-

Marginal cost is the derivative of the cost function. ∴ C(x)=∫ M(x)dx=∫500√(2x+25)dx Put 2x+25=t 2dx=dt ∴ C(x)=∫250√(t)dt C(x)=500(√(t))+c=50 ...

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Standard XII

Mathematics

Equation of a Plane : Normal Form

A manufacture...

Question

A manufacturer's marginal cost function is $\frac{500}{\sqrt{2 x + 25}}$ . Find the cost involved to increase production from $100$ units to $300$ units.

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Solution

Marginal cost is the derivative of the cost function.

$∴ C (x) = \int M (x) d x = \int \frac{500}{\sqrt{2 x + 25}} d x$

Put $2 x + 25 = t ⟹ 2 d x = d t$
$∴ C (x) = \int \frac{250}{\sqrt{t}} d t$
$C (x) = 500 (\sqrt{t}) + c = 500 (\sqrt{2 x + 25}) + c$
where $c$ is constant1

$C (100) = 500 (\sqrt{225}) + c = 7500 + c$

and $C (300) = 500 (\sqrt{625}) + c = 12500 + c$

$C (300) - C (100) = 5000$ Rs.

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A manufacturer's marginal cost function is 500√2x+25. Find the cost involved to increase production from 100 units to 300 units.

Marginal cost is the derivative of the cost function.∴C(x)=∫M(x)dx=∫500√2x+25dxPut 2x+25=t⟹2dx=dt∴C(x)=∫250√tdtC(x)=500(√t)+c=500(√2x+25)+c where c is constant1C(100)=500(√225)+c=7500+cand C(300)=500(√625)+c=12500+cC(300)−C(100)=5000 Rs.

A manufacturer's marginal cost function is $\frac{500}{\sqrt{2 x + 25}}$ . Find the cost involved to increase production from $100$ units to $300$ units.