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- This topic has 3 replies, 2 voices, and was last updated 1 year ago by John Moffat.

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- August 30, 2022 at 8:29 pm #664707
Hi there

Question on J Farms Ltd from Kaplan in relation to minimising costs.

Details – Jfarms ltd can buy two types of fertilisers which contain following % of chemicals,

Type X – Nitrates 18%, Phosphates 5%, Potash 2%

Type Y – Nitrates 3%, Phosphates 2%, Potash 5%

For a certain crop the following minimum quantities (Kg) are required:

Nitrates 100Kg, Phosphates 50Kg, Potash 40Kg

Type X costs $10 per kg and type y costs $5 per kg. J farms currently buys 1000Kg of each type and wishes to minimise its costs on fertilisers.

I was fine with tasks A and partly B but got stuck on finding the optimal solution.

I didn’t understand how to get to the following figures;

Point B – Solving 0.18x + 0.03y = 100Kg & 0.05x + 0.02y = 50

This gives x = 238.10 and y = 1904.80 (How were these figures calculated??)Objective function is Z = 10x + 5y

X is Type X

Y is Type YAugust 31, 2022 at 6:21 am #664725Have you watched my free lectures, because I explain in the lectures how to solve two simultaneous equations together 🙂

August 31, 2022 at 7:58 am #664734I have yes thanks, but your lecture didn’t cover example of when the objective is to minimise costs.

Can you help with this question?

Kind Regards

August 31, 2022 at 3:47 pm #664757I understood from your first post that you were happy at arriving at the equations at point B and that your problem was in solving the two equations together. For that it makes no difference whether it is maximising or minimising.

I cannot check the equations themselves because I do not have the Kaplan Kit (only the BPP Revision Kit).You can solve the equations together in various ways (if you were taught a different way at school and remember it, then do it that way – all methods give the same final answer), What I do is as follows:

Multiply the second equation by 1.5 (so as to get the same number of y’s in both equations.

This gives: 0.075x + 0.03y = 75

If you subtract each term in this equation from each term in the other equation, then you get:

0.105x + 0 = 25

So x = 25/0.105 = 238.10

Put this in either equation and if you put it in the first equation you get:

42.858 + 0.03y = 100

So y = 1904.8

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