Question

Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C'(x) = `x^2/200 + 4`

Answer 1

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