The total cost $C (x)$ in Rupees associated with the production of $x$ units of an item is given by $C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000$ .
Find the marginal revenue when $x = 17.$

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Solution

Marginal cost is the rate of change of total cost with respect to output.

$∴$ Marginal cost (MC) $= \frac{d C}{d x} = 0.007 (3 x^{2}) - 0.003 (2 x) + 15$

$= 0.021 x^{2} - 0.006 x + 15$

Now When $x = 17$ ,
MC $= 0.021 (17^{2}) - 0.006 (17) + 15 = 0.021 (289) - 0.006 (17) + 15$
$= 6.069 - 0.102 + 15 = 20.967$
Hence, when $17$ units are produced, the marginal cost is Rs. $20.967.$

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Similar questions

The total cost C(x) in rupees associated with the production of x units of an item is given by $C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000$ .

Find the marginal cost when x=17 units are produced.

The total cost C (x) in Rupees associated with the production of x units of an item is given by

Find the marginal cost when 17 units are produced.

C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000.

C_{(x)}

R_{(x)}

x

C (x) = 0.1 x^{2} + 30 x + 1000

R (x) = 0.2 x^{2} + 36 x - 100

x = 20

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