Plug and play type McK math question

Question

1) What combination of lines would you pick for each scenario (new factory) vs (expansion) to produce 240K tons and minimize cost. 2) Based on these combinations, which option (new factory vs expansion) would you recommend?

Example Answer for part 1) 2 lines of type 1 and 1 line of type 2 (cost 110M, production ~252K)

Is there a better way to solve such plug and play type questions instead of trying different combinations of 3 lines, 2 lines, 1 line 0 line of each type ..and finding cost / production for each combination? This is still doable for part 1) for the (new) facility since there's a 3 line limit but for (expansion), since any combination of lines are possible, how do you not waste time trying different combinations?

How to approach such plug and play problems in general to save time?

Answer 1

You don't have to try every possible combination. You have to order the options from most effective to least effective from a cost per unit perspective and then do as much of the best as you can, then of the 2nd one, and so on, until you reach the desired capacity. If you have excess capacity, then you compare with the closest alternatives of using more of the lower priority factory (until going to a lower priority does not yiled a better result).

In this case you would have:

Option 1: 3 Type 1 ($130M investment, 299k). A lot of excess capacity.

Then you compare with the closest options as you have spare capacity:

Option 2: 2 T1 and 1 T2 is better ($110M investment, 259k*).
Option 3: 1 T1 an 2 T2 doesn't work.
Option 4: 2 T1 and 1 T3 also doesn't work, so no need to go further.

Option 2 it is!

*I believe you incorrectly calculated this number (8.3*12*2+5*12=259.2)

Answer 2

Hi there,

Pedro gave a great answer, so no need to repeat the answer here.

Just remember, for all math questions you get think realyl critically about “what am I trying to solve for”.

Take that 30 seconds to really think through what you need, have, and don't have. Take time to setup a structure that works in your favor to simplify the problem.

The more you can make math simple, the less time you waste and the fewer mistakes you'll make from brute force attempts!