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Question
Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C'(x) = `x^2/200 + 4`
Solution
Marginal cost C'(x) = `x^2/200 + 4`
Cost functon C = `int "C'" (x) "d"x`
C = `int (x^2/200 + 4) "d"x`
C = `int 1/200 (x^3/3 + 4x) + "k"`
C = `[x^3/600 + 4x] + "k"`
Where x = 0
C = 0
⇒ k = 0
∴ C = `[x^3/600 + 4x]` ........(1)
When x = 200
Equation (1)
⇒ C = `[(200)^3/600 + 4(200)]`
= `[8000000/600 + 800]`
= 13333.33 + 800
∴ Cost of producing 200 air conditioners
= ₹ 14133.33
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