# 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

Sum

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.

#### Solution

Revenue = Price × Demand

∴ R = p × x

∴ R = (10800 - 4x2)x

∴ R = 10800 - 4x3

∴ "dR"/"dx" = 10800 - 12"x"^2 = 12(900 - "x"^2)

Since revenue R is an increasing function,

"dR"/"dx" > 0

∴ 12(900 - x2) > 0

∴ 900 - x2 > 0

∴ 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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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.4 | Q 5.2 | Page 112