Hi Arshan,
It is nice to meet you :)
I've been puzzling over this questions.
It is late - I am making excuses for the fact that my logic may be totally wrong... BUT
I divided all the number by 25 just to make them smaller and easier to work with:
Since the sugar in the 3 cakes is in the ratio 3:2:1
and the sale price of each cake is in the ratio 6:4:2
(The ratios are the same but dollars is twice as big as grams.)
The maximum amount of sugar is 280*25g
So the maximum sale price must be no more than $560*25 = $14000
I drew this graph to help me. I used x y and z for the number of A,B and C cakes produced.
https://www.desmos.com/calculator/bmfpvxwkoc
The maximum sale price is on the green line but it must also be in the shaded region so it seems to me that the maximum sale price is where between A=80, B=0 and C=40 and A=40, B=80 and C=0 as shown on the graph
BUT
to answer this question you do not need to understand all that because it only wants the maximum profit.
OK Maximum sale price is $14000 so
Max profit = 30% of 14000 = $4200
That is what I think anyway. :)