Acompany has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by c(x)=0.2x^2-0.6x+2.250, where c(x) is in hundreds of dollars. what is the minimum average cost per dulcimer and how many dulcimers should be built to achieve that minimum?

The minimum average cost per dulcimer is 150 and the minimum cost is $180.

Step-by-step explanation:

The given cost function is

Differentiate the function C(x) with respect to x.

Equate C'(x)=0, to find the critical values.

Divide both sides by 0.4.

Differentiate the function C'(x) with respect to x.

At x=1.5

The value of double derivative is positive. It means the function is minimum  at x=1.5 hundred.

1.5 hundred = 150

Substitute x=1.5 in the given function to find the minimum average cost.

The minimum cost is 1.8 hundred dollars.

1.8 hundred dollars = $180

Therefore, the minimum average cost per dulcimer is 150 and the minimum cost is $180.

The minimum average cost per dulcimer = $ 180

The number of dulcimers should be built to achieve that minimum =150

Step-by-step explanation:

Given : A company has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by

, where C(x) is in hundreds of dollars.

Now, differentiate the above function with respect to x, we get

                                       (1)

Put C'(x) =0, we get

Again differentiate (1) w.r.t. x , we get

By second derivative test , we have the value of x where C(x) is minimum=1.5

Hence, the minimum average cost per dulcimer = $ 180

The number of dulcimers should be built to achieve that minimum =150