I have been asked a question by an indonesian student. This is the original question.

nilai maksimum f(x,y)=4x+12y pada x+2y<8;3x+2y<12;x>0;y>0 adalah

I ran this through 2 translators and they both gave this

The maximum value of f (x, y) = 4x +12 y on x +2y <8; 3x +2y <12; x> 0; y> 0 is

I am not sure what this means.

I assume it means find the maximum value of 4x+12y given that all the other inequalities are constraints

I have graphed the restricted area and

I have looked at the value of 4x+12y on each of the intersection points And the highest value is 48 at (0,4)

I think this is the answer but I think i should have a much better argument as to why.

Would anyone like to offer any suggestions/help?

Thanks.