On a particular day, three Machines, \(A, B\) and \(C,\) which produce a product, \(P,\) can be used simultaneously, to

[Vincen]

On a particular day, three Machines, \(A, B\) and \(C,\) which produce a product, \(P,\) can be used simultaneously, to produce \(100\) units of \(P.\) Each Machine cannot produce more than \(40\) units in a day. The cost of production per unit of product \(P\) by \(A, B\) and \(C\) are \(\$20, \$10\) and \(\$5,\) respectively. What is the ratio of the minimum cost to the maximum cost incurred, if all \(100\) units of \(P\) are to be produced in a single day?

A. \(\dfrac14\)
B. \(\dfrac12\)
C. \(\dfrac{13}{20}\)
D. \(\dfrac{10}{13}\)
E. \(\dfrac{13}{10}\)

Answer: D

Source: e-GMAT