Question

For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N units in one hour, where N is a positive integer?
(A)12 + 50N.
(B)12 + 2N.
(C)62N.
(D)37N.
(E)25N.

Answer 1

Answer:

(B) 12 + 2N

Explanation:

For every 25 units produced per hour, the factory workers requirement is expressed as shown below.

25 units = 1 Assembly line worker + 12 Managers

Note that the assembly line workers increase for every 25 units produced, whereas the number of managers is fixed irrespective of the number of units produced.

Therefore, to produce 50N units, the number of assembly line workers that will be needed

= $\frac{50N units}{25 units} * 1 Assembly Line Worker$

= 2N Assembly Line Workers

(we can say that since there are ($\frac{50N}{25}$ =) 2N multiples of 25 in 50N units, there will be 2N multiple of assembly line workers needed to produce 50N units)

Since the total number of managers remain fixed, the total number of workers needed to produce 50N units is therefore

= 12 managers + 2N assembly line workers

=12 + 2N.