Stuck on this question about maximizing subject to

[rinnyfer]

Hi all, i'm stuck on this question and was hoping for some help and explanations.

Maximize	z=2x+4y
Subject to	x+4y≤28 6x+3y≤42 x≥0 y≥0

Maximum is: ____ at x= _____, y=_____

 

[Deleted member 4993]

Hi all, i'm stuck on this question and was hoping for some help and explanations.

Maximize	z=2x+4y
Subject to	x+4y≤28 6x+3y≤42 x≥0 y≥0

Maximum is: ____ at x= _____, y=_____

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[Harry_the_cat]

Have you at least drawn a graph of the critical area?

 

[HallsofIvy]

This looks like an exercise in "linear programming", finding max and min values of a linear function on a polygon. The basic rule for such problems is that the max or min of a linear function on a convex polygon always occurs at one of the vertices. That is why Harry the cat is suggesting that you first draw a graph. Where do the lines x= 0, y= 0, x+ y=28, and 6x+ 3y= 42 intersect?