A company has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by C(x)=0.3x^(2)-2.7x+7.775, where C(x) is hundreds of dollars. What is the mimimum average cst per dulcimer and how many dulcimers should be built to achieve that minimum?

4.5 hundreds dulcimers should be build to achieve the minimum  average cost per dulcimer $ 1.7 hundreds.

Step-by-step explanation:

The average cost per dulcimer can be estimated by

C(x)=0.3x² -2.7x+7.775

where C(x) is hundreds of dollar, x hundred dulcimers are built.

C(x)=0.3x² -2.7x+7.775

Differentiating with respect to x

C'(x)=0.6x-2.7

Again differentiating with respect to x

C''(x)=0.6

For maximum or minimum C'(x)=0

0.6x-2.7=0

⇒0.6x=27

⇒ x= 4.5

Now

Since at x= 4.5 , C''(x)>0, So, the average cost per dulcimer is minimum.

C(4.5)= 0.3(4.5)²-2.7×4.5 +7.775×

        =1.7

4.5 hundreds dulcimers should be build to achieve the minimum  average cost per dulcimer $ 1.7 hundreds.

x/3-10=8

x/3=18

x=48