Linear Programming, Corner Points?

Question

1. Solve the following LP problem by enumerating the corner points.

MAX! 3X1+4X2


X1 <=12
X2 <=10
4X1+6X2 <=72
X1, X2 >=0


How does one complete this?

Answer 1

one way is to draw a quick graph of (x1 v x2) -- (x1 for x, x2 for y) -- to get a sense of the solution space.



just draw the regions on the graph, then make a note of which lines/curves intersect.



then use the given equations to figure out exactly what values of (x1,x2) represent the intersection points.



the use that list of intersection points to plug into the expression for the optimization criteria

[presumably MAX! 3 x1 + 4 x2]



then choose the greastest (or least) value of the optimization criteria from the list.



the set of values {x1,x2, f(x1,x2)} represents the solution of the LP problem.

Answer 2

i'm now not too conscious of linear programming. to locate the nook factors. x+5y <=60 evaluate x+5y = 60 locate the x-intercept and y-intercept whilst x=0, y=12 whilst y=0, x= 60 Draw a line connecting these intercepts (0,12) and (60,0) Do the comparable ingredient for the diverse constraints. I extremely have enclosed an instance.