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प्रश्न
The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing
उत्तर
Let C be the total cost function and R be the revenue
∴ C = 180 + 4x
Now, Revenue = Price × Demand
∴ R = P × x = (240 – x)x
∴ R = 240x – x2
∴ `"dR"/("d"x)` = 240 – 2x
= 2(120 – x)
Since revenue R is an increasing function, `"dR"/("d"x)` > 0
∴ 2(120 – x) > 0
∴ 120 – x > 0
∴ 120 > x
∴ x < 120
∴ The revenue is increasing for x < 120.
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