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:
Atmospheric Nitrogen
A component of the Earth's atmosphere, making up about 78% by volume, primarily in the form of nitrogen gas (N2).
Organic Nitrogen Compounds
Chemical compounds that contain carbon and nitrogen, playing various roles in the metabolism of living organisms.
Rain Shadow
An area that has very little precipitation, found on the downwind side of a mountain range. Deserts often occur in rain shadows.
Windward Side
The side of a mountain or island that faces the direction from which the wind is coming, often receiving more rainfall.
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