Question

Score: 2 of 4 pts 3 of 3 (3 complete) v HW Score: 52%, 5.2 of 10 pts %) Problem B.29 Question Help Consider Paul Jordan's following linear programming formulation: Minimize Ν $1X1 + $5X2 1X1 + 3X2 8X1 + 2X2 3X1 + 2X2 1x2 X1, X220 90 160 2 120 s 65 (C1) (C2) (C3) (CA) ΙΛ X2 a) On the graph on right, constraints C1, C2, C3, and C have been plotted. Using the point drawing tool, plot all the corner points for the feasible area. o c2 C3 | 20 30 40 50 60 0 10 70 NC1 80 90 100 X1

Answer 1

a)

Graphical representation is following:

+ rn « -80 1x + 3y > 90 (3.75, 65) XX 8x + 2y > 160 -60 X 3x + 2y > 120 (8,48) y<65 M x + 5y = 90 (25.714, 21.429) -101 -20 -10 0 10 20 30 50 60 70 80 110 120 130 140 150 160 (90,0) --107

Feasible region is the shaded region, which is bounded on one side by points as highlighted on the graph and unbounded towards infinity X1-axis

Value of objective function is minimum at point (90,0)

Therefore, optimal solution is:

X1 = 90

X2 = 0

Objective value = 1*90+5*0 = 90