1. Show that the following LP has altermative optimal solutions; find three of them. max z = -3x, + 6x2 S.L. Sx, + 7x, s 35 -X + 2x s 2 2 Find all optimal solutions to the following LP: max z- 3x, + 3x2 s.t. x + x2 s I All x, 20 3 Suppose you have found this optimal tableau (Table 17) for a maximization problem. Use the fact that each nonbasic variable has a strictly positive coefficient in row 0 to show that x, = 4, x2 = 3, 51 = sz = 0 is the unique optimal solution to this LP. (Hint: Can any extreme point having s, >0 or s2 > 0 have z= 10?) TABLE 17 rhs 3. 10 0. 3. 4 3 4 Consider an LP with the optimal tableau shown in Table 18. a Does this LP have more than one bfs that is optimal? b How many optimal solutions does this LP have? TABLE 18 ths 1 -1 -2 3. 223 21, 1. Show that the following LP has altermative optimal solutions; find three of them. max z = -3x, + 6x2 S.L. Sx, + 7x, s 35 -X + 2x s 2 2 Find all optimal solutions to the following LP: max z- 3x, + 3x2 s.t. x + x2 s I All x, 20 3 Suppose you have found this optimal tableau (Table 17) for a maximization problem. Use the fact that each nonbasic variable has a strictly positive coefficient in row 0 to show that x, = 4, x2 = 3, 51 = sz = 0 is the unique optimal solution to this LP. (Hint: Can any extreme point having s, >0 or s2 > 0 have z= 10?) TABLE 17 rhs 3. 10 0. 3. 4 3 4 Consider an LP with the optimal tableau shown in Table 18. a Does this LP have more than one bfs that is optimal? b How many optimal solutions does this LP have? TABLE 18 ths 1 -1 -2 3. 223 21,