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Question

Manufacturer can sell x items at a price of rupees 5-x100 each. The cost price is Rs x5+500. Find the number of items he should sell to earn maximum profit.

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Solution

Profit =S.P. - C.P.P=x5-x100-500+x5P=5x-x2100-500-x5dPdx=5-x50-15For maximum or minimum values of P, we must havedPdx=05-x50-15=0245=x50x=24×505x=240Now, d2Pdx2=-150<0So, the profit is maximum if 240 items are sold.

Disclaimer: The solution given in the book is incorrect. The solution here is created according to the question given in the book.

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