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For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the values of x for which Revenue is increasing. - Mathematics and Statistics

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Question

For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the values of x for which Revenue is increasing.

Sum
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Solution

Revenue = Price × Demand

∴ R = p × x

∴ R = (10800 - 4x2)x

∴ R = 10800x - 4x3

∴ `"dR"/"dx" = 10800 - 12"x"^2`

Since revenue R is an increasing function,

`"dR"/"dx" > 0`

∴ `10800 - 12"x"^2` > 0

∴ 10800 > 12 x2 

∴ `10800/12` > x2

∴ 900 > x2 

∴ x2 < 900

∴ - 30 < x < 30

∴ x > - 30 and x < 30

But x > - 30 is not possible     ....[∵ x > 0]

∴ x < 30

∴ The revenue R is increasing for x < 30.

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Chapter 4: Applications of Derivatives - Exercise 4.4 [Page 112]

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