Question

The total cost, in dollars, to order x units of a certain product is modeled by C(x)=5x2+320. According to the model, for what size order is the cost per unit a minimum?

Answer 1

It's 8

Explanation:

Answer 2

The minimum cost C(x) = 320 dollars

Explanation:

Step(i):-

Given that the function C(x) = 5 x² + 320 ...(i)

Differentiating equation (i) with respective to 'x', we get

C¹(x) = 5 (2x) + 0

C¹(x) = 10 x..(ii)

Equating zero

C¹(x) = 0

⇒ 10 x=0

⇒ x =0

Step(ii):-

Again differentiating equation (ii) with respective to 'x',we get

C¹¹(x) = 10 (1) = 10 > 0

The total cost C(x) is minmimum at x=0

The minimum cost

C(x) = 5 x² + 320

put x= 0

C(x) = 0 + 320

C(x) = 320