Follow the instructions of Prob. 12.7-3 for the IP model of Prob. 12.5-2

Prob. 12.7-3

Reconsider the IP model of Prob. 12.5-1.

(a) Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve this problem by hand. For each subproblem, solve its LP relaxation graphically.

(b) Now use the interactive routine for this algorithm in your OR Courseware to solve this problem.

(c) Check your answer by using an automatic routine to solve the problem.

Prob. 12.5-1

Consider the following IP problem.

(a) Solve this problem graphically.

(b) Solve the LP relaxation graphically. Round this solution to the nearest integer solution and check whether it is feasible Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i.e., by rounding each noninteger value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate Z. Are any of these feasible rounded solutions optimal for the IP problem?

Prob. 12.5-2

Follow the instructions of Prob. 12.5-1 for the following IP problem.

Prob. 12.5-1

Consider the following IP problem.

(a) Solve this problem graphically.

(b) Solve the LP relaxation graphically. Round this solution to the nearest integer solution and check whether it is feasible Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i.e., by rounding each noninteger value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate Z. Are any of these feasible rounded solutions optimal for the IP problem?