A newspaper company currently sells 20000 newspapers per day. When it sells one newspaper at ₹5, it makes a profit of ₹2 per paper. It is observed that if the selling price of a newspaper is increased by ₹ x , then the number of newspapers sold per day decreases by 2000 x . What should be the selling price per paper (in ₹) to obtain the maximum profit?
Answers
Given : A newspaper company currently sells 20000 newspapers per day. When it sells one newspaper at ₹5, it makes a profit of ₹2 per paper. It is observed that if the selling price of a newspaper is increased by ₹ x , then the number of newspapers sold per day decreases by 2000 x
To Find : What should be the selling price per paper (in ₹) to obtain the maximum profit?
Solution:
A newspaper company currently sells 20000 newspapers per day. When it sells one newspaper at ₹5
Profit = ₹2 per paper
profit = 20000 * 2 = Rs 40000
if selling price of a newspaper is increased by ₹ x
number of newspapers sold per day decreases by 2000 x
Assuming no profit , no loss for paper unsold
Then Profit = ( 20000 - 2000x)(2 + x)
=> P = 40000 - 4000x + 20000x - 2000x²
=> P 40000 + 16000x - 2000x²
dP/dx = 16000 - 4000x
dP/dx = 0
=> 16000 - 4000x = 0
=> x = 4
d²P/dx² = - 4000 < 0
Hence profit is maximum when x = 4
Profit = ( 20000 - 2000x)(2 + x) = 12000 * 6 = 72000
selling price per paper = 5 + 4 = 9 Rs
selling price per paper 9 (in ₹) to obtain the maximum profit
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