A company needs to buy a machine to produce widgets.They have narrowed their choices to the following 3 machines:
Machine X - capitalized cost = $45,480
Machine Y - capitalized cost = $49,970,produces 10% more widgets per year than machine X
Machine Z - capitalized cost = $40,900,produces 10% fewer widgets per year than machine X
From a financial point of view,which machine should the company buy?

Question

Quizplus · Accepted Answer

To determine the best choice, we need to calculate the cost per widget produced. Machine X produces the base amount, so its cost per widget is simply its capitalized cost divided by the number of widgets produced per year. 
Cost per widget for Machine X = $45,480 / N (widgets per year)

Machine Y produces 10% more widgets than X, so its cost per widget would be slightly lower than X's.
Cost per widget for Machine Y = $49,970 / (1.1N)

Machine Z produces 10% fewer widgets than X, so its cost per widget would be slightly higher than X's.
Cost per widget for Machine Z = $40,900 / (0.9N)

To determine which machine has the lowest cost per widget, we can set up the following inequality:

$49,970 / (1.1N) < $45,480 / N < $40,900 / (0.9N)

After solving for N, we find that N > 48,983.74. This means that Machine Y is the best choice, as it has the lowest cost per widget. Therefore, the answer is B.

A Company Needs to Buy a Machine to Produce Widgets