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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.
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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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