1) Solve the following problem graphically. Indicate (a) whetheror not the problem is feasible, (b) whether or not the problem hasan optimal solution, and (c) whether or not the problem isunbounded. If there is a unique optimal solution, specify thevariable values for this solution. If there are 2 alternativeoptimal solutions, give the values for three different optimalsolutions.
max 9x1 + 3x2
s.t. x2 ? 125
? x1 + 2x2 ? 170
3x1 + x2 ? 300
? x1 + x2 ? 20
x1, x2 ? 0
2) PART A) Use the graphical approach to verify that thefollowing problem is unbounded.
max 3x1 ? x2
s.t. ? 2x1 + x2 ? 0
x1 + 2x2 ? 4
3x1 ? 5x2 ? 10
x1, x2 ? 0
PART B) Suppose you change the third constraint to “ax1 ? 5x2 ?10,” where a is nonnegative value. For what values of a does theproblem (i) remain unbounded, (ii) have an optimal solution, and(iii) become infeasible?
