Question

A manufacture’s marginal revenue function is given by MR = 275 – x – 0.3x². Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units

Answer 1

MR = 275 – x – 0.3x²

The increase in the manufactures total revenue 20

T.R = `int "MR"  "d"x` = (275 – x – 0.3x²) dx

T.R = `int_10^20 "MR"  "d"x` = (275 – x – 0.3x²) dx

= `[275x - x^2/2 - (0.3) x^3/3]_10^20`

= `[275x - x^2/2 - 0.1 (x^3)]_10^20`

= `[275(20) - (20)^2/2 - 0.1 (20)^3] - [275(10) - (10)^2/2 - 0.1(10)^3]`

= [5500 – 200 – 0.1(8000)] – [2750 – 50 – 0.1(1000)]

= [5500 – 200 – 800] – [2750 – 50 – 100]

= 4500 – 2600

= ₹ 1900