1.

The equality lines for the following constraints are shown in the graph below: 8x + 3y IA 24 10r + 16y 2 80 -2x + 8y 8 7 6 G 5 4 3 B D F A E 6 a The feasible region is the area represented by the letter ABCDEFG 0 0 0 0 0 0 0The tables below show prior, conditional, joint, marginal, and posterior probabilities for 3 states of nature: Good, Fair, and Poor. Encouraging and Discouraging are the possible forecasts of sample information. Encouraging Prior Conditional Joint Posterior Good 0.25 0. 14 0.035 0.062 Fair 0.Z 0.32 0.064 0.114 Poor 0.5 J.8 0.462 0.824 Discouraging Prior Conditional Joint Posterior Good 0.25 0.86 0.215 D.49 Fair 0.2 0.6 0.136 0.31 Poor 0.5 0.16 0.088 0.2 Use the given tables to determine the following probabilities: a) P(Fair) = b) P(Encouraging | Good) = c) P(Discouraging | Good) d) P(Discouraging and Poor) e) P(Encouraging and Poor) () P(Good | Discouraging) = g) P(Poor | Encouraging) = h) P( Encouraging) = > Next QuestionMinimize Z = 15x + 73y 2x + 4y 2 40 8x + 5y 72 Subject to 17 0 a) Graph the feasible region for the constraints. Drawing the feasible region requires 3 clicks for each constraint on the graph. Use the first two clicks to draw the line and the third click to select the region satisfying the constraint. 16 14 12 10. 2 2 10 12 14 16 18 20 22 Clear All Draw: b) The optimal solution occurs at z = and y = The optimal objective function value Z = > Next