Minimize:z=x+3y subject to: x+y?10 5x+2y?20 -x+2y?0 x?0 y?o Min value is__ when

Question

Minimize:z=x+3y
subject to:
x+y?10
5x+2y?20
-x+2y?0
x?0
y?o

Min value is__
when x=__
and y=__

Explanation / Answer

draw a set of axes get all your constraints into y=mx+b form draw all 3 lines in the range specified and shade the appropriate side your answer will be staring at you. for the first one: x + y < 10 becomes y = -x + 10 you draw this line and shade everything to the left between the line and the axes (you stop at the axes because you have constraints x, y > 0) 5x + 2y > 20 becomes y = -5/2x + 10. shade to the right now (because it's a > symbol) -x + 2y > 0 becomes y = 1/2x. shade to the right again you now will have a region that was shaded from all 3 steps. in a perfect world, this region would be a point, and that would be your answer. However, usually, it's a polygon with a number of end points. You simply write down these points and plug them into your equation Z=x+3y, and whichever one is the minimum is your answer

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