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प्रश्न
The total cost function for production of x articles is given as C = 100 + 600x – 3x2 . Find the values of x for which total cost is decreasing.
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उत्तर
Given, the cost function is
C = 100 + 600x - 3x2
∴ `"dC"/"dx" = 0 + 600 - 6"x"`
= 600 - 6x
= 6(100 - x)
Since total cost C is a decreasing function,
`"dC"/"dx" < 0`
∴ 6(100 - x) < 0
∴ 100 - x < 0
∴ 100 < x
∴ x > 100
∴ The total cost is decreasing for x > 100.
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Solution: Total cost C = 40 + 2x and Price p = 120 − x
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∴ π = `square`
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`("d"pi)/("d"x)` > 0
∴ Profit is increasing for `square`
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∴ x = 120 – p
Differentiating w.r.t. p,
`("d"x)/("dp")` = `square`
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