A manager must decide which type of machine to buy, A$,$ B$,$ or C$.$ Machine costs $($per individual machine$)$ are as follows:

Machine Cost

A $ $50,000$

B $ $40,000$

C $ $70,000$

Product forecasts and processing times on the machines are as follows:

PROCCESSING TIME PER UNIT $($minutes$)$

Product Annual

Demand A B C

$112,000212$

$221,000263$

$311,000245$

$425,000352$

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a$.$ Assume that only purchasing costs are being considered. Compute the total processing time required for each machine type to meet demand, how many of each machine type would be needed, and the resulting total purchasing cost for each machine type. The machines will operate $10$ hours a day, $230$ days a year.