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?

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.

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

320.39

Your answer should be 1/3. i hope i could ! good luck : )