Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf f(r) = 2e^-2r on (0 ,∞ )

x=7

Step-by-step explanation:

The cost to produce a product is modeled by the function  , where x is the number of products produced.

We have to determine the minimum cost of producing this product.

Since,

Now, consider the equation

Dividing the above equation by 5, we get

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing .

Since, coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting  from the above equation.

Now, we have to determine the minimum cost to produce the product.

Since,

Now, let f'(x)=0

Therefore, x=7

Now, consider  which is greater than 0.

Therefore, x= 7 is the minimum cost.

The minimum cost to produce the product is $7.