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Manufactures can sell x items at a price of Rs (5 - \(\frac{x}{100}\)) each. The cost price is Rs  (\(\frac{x}{5}\) + 500). Find the number of items he should sell to earn maximum profit.

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Best answer

Cost Price (CP) for producing x amount = 500 + \(\frac{x}{5}\)

Selling Price (SP) per producing x amount = 5 - \(\frac{x}{100}\)

Selling Price (SP) per producing x amount = 5x - \(\frac{x^2}{100}\)

Profit P = SP - CP

x = 240

Therefore,

\(\frac{d^2P}{dx^2}\) = \(-\frac{1}{50}\) < 0

Thus, 

x = 240 is a point of maxima. 

Thus for maximum profit, 

x should be 240.

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