Sum
A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing.
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Solution
Let C be the total cost function.
∴ C = 40 + 2x
Revenue = Price × Demand
∴ `"R" = "p" × "x" = (120 - "x") * "x"`
∴ R = 120x - x2
∴ `"dR"/"dx" = 120 - 2"x" = 2(60 - "x")`
Since revenue R is an increasing function, `"dR"/"dx" > 0`
∴ 2(60 - x) > 0
∴ 60 - x > 0
∴ 60 > x
∴ x < 60
∴ The revenue R is increasing for x < 60.
Concept: Application of Derivatives to Economics
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