--, P. Z 0 0 3 0 Problem 8: Table 1 depicts a simplex tableau below for a maximization LP, in which some of the numbers have been replaced by constants P1, P2, Table 1: Simplex Tableau bv X1 X2 S1 S2 S3 S4 RHS Z 1 0 0 P1 46 S1 0 0 0 1 P2 -1/7 46/7 X1 0 0 0 -2/7 1/7 Ps S2 0 0 0 0 1 P3 -1 13 X2 0 0 1 0 0 -1/7 P4 P6 In addition, suppose the plot in Figure 1 depicts the feasible region for the same maximization LP. The slack variables S1, ..., S4 have been labeled on the plot to indicate where they are nonnegative. Figure 1: Plot of Feasible Region 1 0 S3 201 $2 S1 S4 B 10 D H F 10 20 21 G 3 Use Table 1 and Figure 1 to answer the following questions. Part a: Among the solutions labeled A, B, ..., K in Figure 1, which one corresponds to the solution represented in the simplex tableau of Table 1? Part b: Based upon your answer to part a, what is the smallest integer that is greater than or equal to Ps? What is the smallest integer that is greater than or equal to po? (Note: You should not need to do any calculations for this part.) Part c: Suppose the objective function is "maximize 5x + 4x2." According to Figure 1, should the value of p, be positive, negative, or zero? Explain why in no more than two sentences. Part d: According to Figure 1, should the value of pz be positive, negative, or zero? Explain why in no more than two sentences. --, P. Z 0 0 3 0 Problem 8: Table 1 depicts a simplex tableau below for a maximization LP, in which some of the numbers have been replaced by constants P1, P2, Table 1: Simplex Tableau bv X1 X2 S1 S2 S3 S4 RHS Z 1 0 0 P1 46 S1 0 0 0 1 P2 -1/7 46/7 X1 0 0 0 -2/7 1/7 Ps S2 0 0 0 0 1 P3 -1 13 X2 0 0 1 0 0 -1/7 P4 P6 In addition, suppose the plot in Figure 1 depicts the feasible region for the same maximization LP. The slack variables S1, ..., S4 have been labeled on the plot to indicate where they are nonnegative. Figure 1: Plot of Feasible Region 1 0 S3 201 $2 S1 S4 B 10 D H F 10 20 21 G 3 Use Table 1 and Figure 1 to answer the following questions. Part a: Among the solutions labeled A, B, ..., K in Figure 1, which one corresponds to the solution represented in the simplex tableau of Table 1? Part b: Based upon your answer to part a, what is the smallest integer that is greater than or equal to Ps? What is the smallest integer that is greater than or equal to po? (Note: You should not need to do any calculations for this part.) Part c: Suppose the objective function is "maximize 5x + 4x2." According to Figure 1, should the value of p, be positive, negative, or zero? Explain why in no more than two sentences. Part d: According to Figure 1, should the value of pz be positive, negative, or zero? Explain why in no more than two sentences