some doubts?

Question

here is a problem with solution
http://docs.google.com/Doc?id=dc83hzcs_222d455g8

i have some doubts

can you please clarify ?

Answer 1

I have doubts too. I do agree with the solver that we want to minimize the production of B. Product B uses up more time per unit of each machine, compared with Product A, so there is no advantage to producing more of B than we have to.

But it seems to me we can produce 2 of A and 1 of B, for a total of 3 units.

time spent on M1: 2(6) + 1(10) = 22 hrs <23 hrs available
time spent on M2: 2(3) + 1(8) = 14 hrs < 15 hrs available

Answer 2

1) Minimize production of part B to maximize overall production,l simply because it takes longer to produce. This makes intuitive sense if you think about the overall time to produce part A and part B.

2) The table is written so that during the hour listed, the machine is used for the part indicated in that table. When machine M1 is used for hours 1-10 on part B, it means hours one THROUGH 10. Hour one is completely dedicated, hour two is completely dedicated, hour three is completely dedicated, and so on, ... hour nine is completely dedicated, and hour ten is completely dedicated to producing part B. Hour eleven, coming after this, is then used on part A.

3) In order to get the maximum number of parts, machine M2 starts on its portion IMMEDIATELY following completion of the part on machine M1. This is permitted.