Question

The average cost per hour in dollars of producing x riding lawn mowers is given by the following.

Upper C overbar left parenthesis x right parenthesis equals 0.5 x squared plus 23 x minus 216 plus StartFraction 2600 Over x EndFractionC(x)=0.5x2+23x−216+
2600
x
​(a) Use a graphing utility to determine the number of riding lawn mowers to produce in
      order to minimize average cost.
​(b) What is the minimum average​ cost?

Answer 1

Attached you can find the graph obtained with a graphing utility.

I included only the region where the solution is.

I marked with dotted lines the minimum point and used arrows to indicate its components.

a) the minimum average cost is obtained when you produce 9 riding lawn mowers.

You can check it if you use the formula with three values of x: x =8, x = 9 and x = 10.

Answer: 9

That coordinate is indicated with an arrow.

b) The minimum average cost is obtained when you use the formula for the average cost with x = 9:

C(x) = 0.5*(9)^2 + 23(9) - 216 + 2600/x = 320.39

Answer: 320.39