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?

 The minimum cost       C(x) = 320 dollars

Step-by-step 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        

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