Given the following linear program with the corresponding optimal basis, for what range of values of the objective function for each variable (considered one at a time) will the basis still be optimal? You must consider both the basic and non-basic variables in your answer. Remember, the "certificate of optimality" says that for a basis to be optimal, all non-basic variables must have non-negative reduced cost. For example, if you replaced the cost coefficient of variable a in the first problem (a) with some value $, for what values of $ would this basis still be optimal? What if you replaced the cost coefficients of b? c? d? etc. a) A: 1 0 02 5 1 b: 2 3 30 60 1 1 1 20 50 Optimal basis: {a,b} b) b: A: 1 05 0 2 1 w N 30 60 c: 0 0 2 5 Optimal basis: (a, b) Min 3a + b + 14C + 3e + 6f St: a + 2c - 2d + e = 4 3b + 4c + 12d + 2e +5f = 12 a, b, c, d, e, f>o To check yourself, the optimal solution should be d=0.25, e=4.5 with an objective value of 13.5, and non-basic variables a=b=c=f=0. Given the following linear program with the corresponding optimal basis, for what range of values of the objective function for each variable (considered one at a time) will the basis still be optimal? You must consider both the basic and non-basic variables in your answer. Remember, the "certificate of optimality" says that for a basis to be optimal, all non-basic variables must have non-negative reduced cost. For example, if you replaced the cost coefficient of variable a in the first problem (a) with some value $, for what values of $ would this basis still be optimal? What if you replaced the cost coefficients of b? c? d? etc. a) A: 1 0 02 5 1 b: 2 3 30 60 1 1 1 20 50 Optimal basis: {a,b} b) b: A: 1 05 0 2 1 w N 30 60 c: 0 0 2 5 Optimal basis: (a, b) Min 3a + b + 14C + 3e + 6f St: a + 2c - 2d + e = 4 3b + 4c + 12d + 2e +5f = 12 a, b, c, d, e, f>o To check yourself, the optimal solution should be d=0.25, e=4.5 with an objective value of 13.5, and non-basic variables a=b=c=f=0