Question

The total cost of producing certain
article is C = x2 – 5x + 100, the
average cost of producing 5 such
items is​

Answer 1

$\large\underline{\sf{Solution-}}$

☆ Cost of producing certain articles is given as

$\red{\rm :\longmapsto\:C \: = \: {x}^{2} - 5x + 100}$

We know,

☆ Average Cost is given by

$\bf :\longmapsto\:AC = \dfrac{C}{x}$

$\rm :\longmapsto\:AC = \dfrac{ {x}^{2} - 5x + 100 }{x}$

$\rm :\longmapsto\:AC = \dfrac{ {x}^{2} }{x} - \dfrac{5x}{x} + \dfrac{100}{x}$

$\rm :\longmapsto\:AC = x - 5 + \dfrac{100}{x}$

Now,

☆ Average Cost of producing 5 articles is

$\rm :\longmapsto\:AC_{(x = 5)} = 5 - 5 + \dfrac{100}{5}$

$\rm :\longmapsto\:AC_{(x = 5)} = 20$

Additional Information :-

☆ Marginal cost is given by

$\green{\boxed{ \tt \: MC = \dfrac{d}{dx}C }}$

☆ Marginal Average Cost is given by

$\green{\boxed{ \tt \: MAC = \dfrac{d}{dx}AC }}$

☆ Revenue function is given by

$\green{\boxed{ \tt \:R = px }}$

☆Average Revenue function is given by

$\green{\boxed{ \tt \: AR = \dfrac{R}{x} }}$

☆ Marginal Revenue is given by

$\green{\boxed{ \tt \: MR = \dfrac{d}{dx}R }}$

☆ Break - even point is given by

$\green{\boxed{ \tt \:R = C }}$