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MINIMIZATION., Operation Research

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Consider the LP
min ?? = 50??1 + 100??2
3
??.??. 7??1+2??2=28 2??1+12??2=24 ??1,??2=0
a. A basic solution of the constraint equations of this problem has how many basic variables, in addition to -z? _____
b. What is the maximum number of basic solutions (either feasible or infeasible) which might exist? (That is, how many ways might you select a set of basic variables from the four variables x1 through x4?) _____
c. Find and list all of the basic solutions of the constraint equations.
d. Is the number of basic solutions in (c) equal to the maximum possible number which you specified in (b)? ______
e. How many of the basic solutions in (c) are feasible (i.e. nonnegative)?
f. By evaluating the objective function at each basic solution, find the optimal solution.

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