Solve the following linear program using AMPL/CPLEX with sensitivity output turned on. min 800x1 +880x2 + 960x3 + 960x4 + 960x5 + 960x6 +880x7 s.t. X1 + X4 +x5 + X6 +x7 37 (Monday Constraint) X1 + X2 + X5 + X6 +x7 2 21 (Tuesday Constraint) X1 + X2 + X3 + X6 +x7 238 (Wednesday Constraint) X1 + X2 + X3 + X4 +x7 35 (Thursday Constraint) X1 + X2 + X3 + X4 + X5 31 (Friday Constraint) X2 + X3 + X4 + X5 + X6 24 (Saturday Constraint) X3 + X4 + X5 + X6 +x7 28 (Sunday Constraint) Xi 2 0 for all i = 1,2,...,7 For the purposes of this assignment, you should not restrict your variables to be integer-valued. (Note: It would be reasonable to require integer-valued variables in practice, but doing so would cause us to lose access to the sensitivity information.) For every variable, output the following information: 1. The variable's value in the obtained optimal basic feasible solution (BFS). 2. The variable's reduced cost with respect to the obtained optimal BFS. 3. The variable's current objective function coefficent. 4. The maximum value of the variable's objective function coefficient such that the obtained optimal BFS remains optimal. 5. The minimum value of the variable's objective function coefficient such that the obtained optimal BFS remains optimal. For every constraint, output the following information: 1. The constraint's slack with respect to the obtained optimal BFS. 2. The constraint's shadow price with respect to the obtained optimal BFS. 3. The constraint's current right-hand-side value. 4. The maximum value of the constraint's right-hand-side value such that the obtained optimal basis remains optimal. 5. The minimum value of the constraint's right-hand-side value such that the obtained optimal basis remains optimal You will use this output to answer the remaining questions. QUESTION 1 Suppose you change the right-hand side of the Saturday constraint without changing any of the other parameters. What is the largest you could make this value such that the current basis would remain optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 2 Suppose you change the right-hand side of the Monday constraint without changing any of the other parameters. What is the smallest you could make this value such that the current basis would remain optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 3 What is the shadow price of the Thursday constraint? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 4 By how much will the optimal objective value increase if we increase the right-hand side of the Saturday constraint from 24 to 25? (Enter a numerical value. Your answer must be correct within +/-0.01.) QUESTION 5 With respect to the obtained optimal solution, what is the slack in the Tuesday constraint? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 6 Currently, the objective coefficient for x4 is 960. Suppose we increase the value of this coefficient without changing the value of any other parameters. What is the largest value of this coefficient such that the current basis remains optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) > 1 points Save Answer QUESTION 7 Currently, the objective coefficient for x1 is 800. Suppose we decrease the value of this coefficient without changing the value of any other parameters. What is the smallest value of this coefficient such that the current basis remains optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer Solve the following linear program using AMPL/CPLEX with sensitivity output turned on. min 800x1 +880x2 + 960x3 + 960x4 + 960x5 + 960x6 +880x7 s.t. X1 + X4 +x5 + X6 +x7 37 (Monday Constraint) X1 + X2 + X5 + X6 +x7 2 21 (Tuesday Constraint) X1 + X2 + X3 + X6 +x7 238 (Wednesday Constraint) X1 + X2 + X3 + X4 +x7 35 (Thursday Constraint) X1 + X2 + X3 + X4 + X5 31 (Friday Constraint) X2 + X3 + X4 + X5 + X6 24 (Saturday Constraint) X3 + X4 + X5 + X6 +x7 28 (Sunday Constraint) Xi 2 0 for all i = 1,2,...,7 For the purposes of this assignment, you should not restrict your variables to be integer-valued. (Note: It would be reasonable to require integer-valued variables in practice, but doing so would cause us to lose access to the sensitivity information.) For every variable, output the following information: 1. The variable's value in the obtained optimal basic feasible solution (BFS). 2. The variable's reduced cost with respect to the obtained optimal BFS. 3. The variable's current objective function coefficent. 4. The maximum value of the variable's objective function coefficient such that the obtained optimal BFS remains optimal. 5. The minimum value of the variable's objective function coefficient such that the obtained optimal BFS remains optimal. For every constraint, output the following information: 1. The constraint's slack with respect to the obtained optimal BFS. 2. The constraint's shadow price with respect to the obtained optimal BFS. 3. The constraint's current right-hand-side value. 4. The maximum value of the constraint's right-hand-side value such that the obtained optimal basis remains optimal. 5. The minimum value of the constraint's right-hand-side value such that the obtained optimal basis remains optimal You will use this output to answer the remaining questions. QUESTION 1 Suppose you change the right-hand side of the Saturday constraint without changing any of the other parameters. What is the largest you could make this value such that the current basis would remain optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 2 Suppose you change the right-hand side of the Monday constraint without changing any of the other parameters. What is the smallest you could make this value such that the current basis would remain optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 3 What is the shadow price of the Thursday constraint? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 4 By how much will the optimal objective value increase if we increase the right-hand side of the Saturday constraint from 24 to 25? (Enter a numerical value. Your answer must be correct within +/-0.01.) QUESTION 5 With respect to the obtained optimal solution, what is the slack in the Tuesday constraint? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save Answer QUESTION 6 Currently, the objective coefficient for x4 is 960. Suppose we increase the value of this coefficient without changing the value of any other parameters. What is the largest value of this coefficient such that the current basis remains optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) > 1 points Save Answer QUESTION 7 Currently, the objective coefficient for x1 is 800. Suppose we decrease the value of this coefficient without changing the value of any other parameters. What is the smallest value of this coefficient such that the current basis remains optimal? (Enter a numerical value. Your answer must be correct within +/-0.01.) 1 points Save