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D1 Linear Programming question

Hello there, for a linear programming question, how do I find the objective function if I haven't been given it?

In this question, in part (b)(iii) for example:



Here's the graph:


How do I find the maximum total number of hampers if I haven't been given an objective function to maximize? Is there a way to make an objective function?
Reply 1
You can produce an objective function yourself. Usually it involves some sort of profit on each type of product, so this one is a tad unusual. You want to maximise the number of hampers made. Now, if you make xx basic, yy standard and zz luxury, then you make x+y+zx+y+z total, but you are told that you make the same number of standard hampers as you do luxury hampers so y=zy=z hence the total number made simplifies to x+y+y=x+2yx+y+y=x+2y. This is what you want to maximise, so your objective function would now be P=x+2yP=x+2y. :smile:
Original post by Ktulu666
You can produce an objective function yourself. Usually it involves some sort of profit on each type of product, so this one is a tad unusual. You want to maximise the number of hampers made. Now, if you make xx basic, yy standard and zz luxury, then you make x+y+zx+y+z total, but you are told that you make the same number of standard hampers as you do luxury hampers so y=zy=z hence the total number made simplifies to x+y+y=x+2yx+y+y=x+2y. This is what you want to maximise, so your objective function would now be P=x+2yP=x+2y. :smile:


Splendid. Thank you. :smile:
Reply 3
Original post by Engineering Lad
Splendid. Thank you. :smile:


No problem :smile: In future, read exactly what the paper wants you to maximise, find an expression for it, and voila! You have your function.

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