Question

total cost fuction is C=1200+20x + x²
$1200 + 20x + x {}^{2}$
find the marginal cost when 10 units are produced
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Answer 1

Total cost function :

C(x) = 1200 + 20x + x²

Marginal cost is the rate of change of cost.

$\sf \: Marginal \: cost \: at \: x_0 = (\frac{dC}{dx}) _{x = x_0}$

To find,

Marginal cost when 10 units are produced.

Marginal cost

dC/dx = d/dx ( 1200 + 20x + x²)

dC/dx = 0 + 20 + 2x

dC/dx = 2x + 20

Marginal cost when 10 units are produced.

$( \frac{dC}{dx})_{ \small{x= 10}}=20 + 2(10) \\\\ ( \frac{dC}{dx})_{ \small{x= 10}} = 20 + 20 \\ \\ ( \frac{dC}{dx})_{ \small{x= 10}} = 40$

Marginal cost is 40 when 10 units are produced

Answer 2

Total cost function :

C(x) = 1200 + 20x + x²

Marginal cost is the rate of change of cost.

=dx/dC

x=x

0

To find,

Marginal cost when 10 units are produced.

Marginal cost

dC/dx = d/dx ( 1200 + 20x + x²)

dC/dx = 0 + 20 + 2x

dC/dx = 2x + 20

dx/dC

x=10

=20+2(10)(

dx/dC

x=10

=20+20

DX/DC

x=10

=40

Marginal cost is 40 when 10 units are produced