Question

The total revenue in rupees received from the sale of x units of a product is given by R(x)=20x²+15x+50. Find the marginal revenue when x=15.

Answer 1

Answer:

marginal revenue  is 615  when x=15

Step-by-step explanation:

Marginal revenue is the rate of change of total revenue with respect to number of units sold

R(x)=20x²+15x+50

dR/dX = 40X + 15

When X = 15

then

dR/dX = 40*15 + 15  = 615

marginal revenue when x=15  is 615

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{Marginal \: Revenue = \frac{ Change \: in \: Revenue}{Change \: in \: Quantity } \: \: \: }$

In calculus in terms of derivatives

If R = Total revenue received from the sale of x units of a product

Then

$\displaystyle \sf{Marginal \: Revenue = \frac{ d R}{dx } \: \: \: }$

GIVEN

The total revenue in rupees received from the sale of x units of a product is given by R(x)=20x²+15x+50

TO DETERMINE

The marginal revenue when x = 15

CALCULATION

Here the total revenue in rupees received from the sale of x units of a product is given by

R(x)=20x²+15x+50

Differentiating both sides with respect to x we get

$\displaystyle \sf{\frac{ d R}{dx } = \frac{d}{dx} (20 {x}^{2} + 15x + 50)\: \: \: }$

$\implies \: \displaystyle \sf{\frac{ d R}{dx } = 20\frac{d}{dx} ( {x}^{2} ) +15\frac{d}{dx}( x )+ \frac{d}{dx}(50)\: \: \: }$

$\implies \: \displaystyle \sf{\frac{ d R}{dx } = 40x + 15 \: }$

Now for x = 15

$\implies \: \displaystyle \sf{\frac{ d R}{dx } = (40 \times 15) + 15\: }$

$\implies \: \displaystyle \sf{\frac{ d R}{dx } = 615\: }$

RESULT

Hence the marginal Revenue = 615

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LEARN MORE FROM BRAINLY

Out of the following which are proper fractional numbers?

(i)3/2

(ii)2/5

(iii)1/7

(iv)8/3

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