Resolved: "C(x)=5,000+20x−14x2 is a cost function. Calculate the marginal..."

Lennie Carroll

Answered question

2021-09-07

$C (x) = 5, 000 + 20 x - \frac{1}{4} x^{2}$
is a cost function.
Calculate the marginal average cost when 20

(a), use your result to estimate the total cost when $x = 21$

(b) and calculate the percentage error between this estimate and the actual cost when $x = 21$

StrycharzT

Skilled2021-09-08Added 102 answers

C (x) = 5, 000 + 20 x - \frac{1}{4} x^{2}

\frac{C (x)}{x} = ?

\frac{C (x)}{x}

= \frac{5, 000 + 20 x - \frac{1}{4} x^{2}}{x}

= \frac{5000}{x} + 20 - \frac{1}{4} x

{\overset{―}{C}}^{'} (x) = \frac{d (\frac{5000}{x} + 20 - \frac{1}{4} x)}{d x}

= - \frac{5000}{x^{2}} - \frac{1}{4}

{\overset{―}{C}}^{'} (20) = - \frac{5000}{x^{2}} - \frac{1}{4}

= - 12.5 - 0.25

= - 12.75

And

C (20) = \frac{5000}{20} + 20 - \frac{1}{4} (20) = 265

(a)

\overset{―}{C} (21) = \overset{―}{C} (20) + {\overset{―}{C}}^{'} (20)

= 265 - 12.75

= 252.25

C \frac{21}{21} = 252.25

C (21) = 5297.25

(b)

\underset{E}{C} = 5000 + 20 (21) - \frac{1}{4} {(21)}^{2}

= 5309.75

\frac{5309.75 - 5297.25}{5309.75} \times 100 = 0.24 %

(c)

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