Limiting factor

GDIPIETRO

Hi,
I hope you are all OK and safe.
I would like to ask a question regarding limiting factor, I hope someone can help. Based on the attachment /question that includes also the workings I've got a optimal production rank as T, R, S. How do I calculate the other production plan with the number I have for R, S, T or S, T, R? (often come up in the exam but not sure I do the right calculation for them)
Thanks in advance
G.

PeterC

The maximum you can sell are:
20,000 of R
25,000 of S
8,000 of T

Based on the contribution per labours hour, T is best, R is next best and S is worst.

You have identified that the optimum plan is therefore to make and sell
8,000 of T
20,000 of R
12,000 of S
providing a contribution of £540,000

This is usually all that is asked for, but you also asked about the sub-optimal alternatives

If you were to prioritise in the order R, then S, then T, you would make
20,000 of R, using 40,000 labour hours (20,000x2)
This leaves 60,000 labour hours (100,000-40,000),
which is enough to make 20,000 units of S (60,000/3)
and no hours left to make any of T

The contribution would be
£220,000 from R (20,000x11) and
£280,000 from S (20,000x14)
a total of £500,000

If you were to prioritise in the order S, then T, then R, you would make
25,000 of S, using 75,000 labour hours (25,000x3)
8,000 of T, using 24,000 labour hours (8,000x3)
This leaves 1,000 labour hours (100,000-75,000-24,000),
which is enough to make 500 units of R (1,000/2)


The contribution would be
£350,000 from S (25,000x14),
£152,000 from T (8,000x19) and
£5,500 from R (500x11)
a total of £507,500


I hope this answers your question