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Hardison Incorporated manufactures glass for office buildings in Florida. As a result of age and wear, a critical machine in the production process has begun to produce quality defects. Hardison is considering replacing the old machine with a new machine, either brand A or brand B$.$ The manufacturer has provided Hardison with the following data on the costs of operation of each machine brand at various levels of output:

Output $($square yards$)$ Brand A Estimated Total Costs Brand B Estimated Total Costs

$2,000$ $ $107,000$ $ $130,000$

$4,000135,000170,000$

$8,000190,000210,000$

$16,000235,000270,000$

$32,000290,000310,000$

$64,000472,800402,800$

Required:

$2.$ Use the high$-$low method to determine the cost equation for each brand of machine and use the results to calculate the costs of operating each machine if Hardison's output is expected to be $25,000$ square yards.

$3.$ Using the high$-$low equations from requirement $2,$ calculate the costs of operating each machine if Hardison's output is expected to be $40,000$ square yards and then for expected output of $60,000$ square yards.

$4.$ If Hardison's output is expected to be $40,000$ square yards, which machine should it purchase? At $25,000$ and at $60,000$ square yards?