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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
Solution
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
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