Question

2. Consider the following linear model where c has not yet been defined. Max z = C1x1 + x2 s.t. X1 + X2 <6 X1 + 2.5x2 < 10 X1 2 0,X220 Use the graphical approach that we covered to find the optimal solution, x*=(x,x) for all values of - Sci so Hint: First draw the feasible region and notice that there are only a few corner points that can be the optimal solution. Also remember that if the objective function line reaches a maximum and it includes two adjacent corner points, both of these points and all of the points that create the line that connects them are optimal. There is literally an infinite number of optimal solutions ... but only one optimal objective function value because if you plug in the values of xi and X2 you get the same (max) value. Now, ci controls that slope of the objective function line and this is the critical concept. Go to any of the corner points and some values of c, that make that point the optimal solution. Then ask yourself how much can the slope increase or decrease) that will move the optimal solution to an adjacent corner point. That range is the answer to this question.

Answer 1

so lution GO max 2- Gaitz subject to 24+ 22 56 M+2.582410 4, 227,0. Now we apply Graphical method to find the optimal solution. 24 24+ ez_ max. f 24 +72 26. x 22 0 f M+2.52² 10 - 247 24 h 22 10 + 7 819) 33 100 6,02 A I 123 2 5 6 7 8 9 10 The shaded postion the optimal area .O A BC.

wow solving & 24+ x₂ = C x2= 6.21 27 21 + h 2210 -) *+ (4--1)=0 -> 2+ 45-4 -- 4210 24 = -5 10 * *, - 243 3 3 OABC ele so the corner poret sot the optimal arca (0,0), (6,0)() (0,4) clearly the apt maximum valued attains at 2,2 10 31 222 8 3 i Max Max Z= e, log + for -BLC, 22.