Consider the following discrete nonlinear programming problem.Maximize Z = 
,subject to x1 + x2 ≤ 0.75 and each variable is restricted to the values: 
.
(a)Reformulate this problem as a pure binary integer linear programming problem.
(b)Use the following outline in designing the main features of a branch-and-bound algorithm for solving this problem (and similar problems)directly without reformulation.(1)Specify the tightest possible nonlinear programming relaxation that has only continuous variables,and so can be solved efficiently by nonlinear programming techniques.(2)Specify the fathoming tests.(3)Specify a branching procedure that involves specifying two ranges of values for a single variable.
Definitions:
Loud Work Environment
A workplace characterized by high levels of noise, which can distract employees and decrease productivity.
Cognitive Dissonance
Cognitive dissonance is the psychological discomfort experienced when holding two or more conflicting beliefs, values, or attitudes simultaneously.
Social Loafing
The failure of a group member to contribute personal time, effort, thoughts, or other resources to the group.
Legitimate Emergencies
Situations that are recognized as valid and urgent, requiring immediate attention and action.
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