Auto Assembly Plant........

Let's express auto parts in terms of man-hours 

12 man x 7 days x 9hrs/day / 390 parts = 1.93846 man-hr / part

Now   a)    21 days x 8 hrs/day x ?men /  2340parts = 1.93846 man-hr/part  ???

                168 x ? / 2340 = 1.93846

                   ? =    1.93846 x (2340)/168 = 26.99  = ~ 27 EMPLOYEES

          b)    20 men x 18 days x 7.5 hours / ? parts  = 1.93846 man-hr / part

                                          20 x 18 x 7.5 /1.93846 = ? parts =  1392.85  =  ~ 1393 parts

12 employees working in an auto assembly plant for 7 days at 9 hours per day can produce 390 auto parts.
a) How many employees working for 21 days at 8 hours per day can produce 2340 auto parts?

63 hrs are required to produce  390 parts

2340 parts is 6 times as many  so it should require 6 * 63 =  378 hrs for 12 employees

But we only have 21 * 8 =  168 hrs

So.......the amount of work done by 12 employees for 378 hrs = the amount of work done by x employees for 168 hrs

12 * 378  =  168 * x

4536  = 168 * x     divide both sides by 168

27 = x        so.....we need 27 employees

b) How many auto parts can be produced by 20 employees working for 18 days at 7.5 hours per day?

Using data from the first problem, 12 employees working in an auto assembly plant for 7 days at 9 hours per day can produce 390 auto parts.

390 parts / 63 hrs = 130/21 parts per hr by 12 employees

So.......20 employees can produce  (20/12) (130/21) =  650/63  parts per hr

So  .......18 * 7.5 = 135 hrs   = hrs available

So....the total number of parts produced  for 135 hrs by 20 employees  =

Parts per hour *  hrs available =

(650/63) * 135   =  about 1392.8  parts