Mr.pritesh orders x Mobiles at the price p=2x+32÷x^2-5÷x. How many mobiles should he order for the most economical deal
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Given : Mr.pritesh orders x Mobiles at the price p = 2x + 32/x² - 5/x
To Find : How many mobiles should be ordered for the most economical deal
Solution:
p = 2x + 32/x² - 5/x
mobile ordered = x
Total cost = (2x + 32/x² - 5/x).x
C = 2x² + 32/x - 5
dC/dx = 4x - 32/x²
dC/dx = 0
=> 4x - 32/x² = 0
=> 4x³ - 32 = 0
=> x³ = 8
=> x = 2
d²C/dx² = 4 + 64/x³ > 0
Hence Minimum cost at x = 2
2 mobiles should be ordered for the most economical deal
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