A linear programming problem is given as follows: min Z = −4x1 + x2 Subject to 8x1 + 2x2 ≥ 16 4x1 + 2x2 ≤ 12 x1 ≤ 6 x2 ≤ 4 x1, x2 ≥ 0
A linear programming problem is given as follows:
min Z = −4x1 + x2
Subject to 8x1 + 2x2 ≥ 16
4x1 + 2x2 ≤ 12
x1 ≤ 6
x2 ≤ 4
x1, x2 ≥ 0
IV) What is the solution of the optimization problem? (x1=?,x2=?,z=?) Show your work
V) Which change will make the problem have multiple optimal solutions? If there is more than one answer, choose all.
a) Increase of the coefficient of x1 on the objective function to 4
b) Increase of the coefficient of x1 on the objective function to 2
c) Decrease of the coefficient of x1 on the objective function to -8
d) Increase of the coefficient of x2 on the objective function to -8
e) None
VI) If new constraints, x1≤4 and x2≤6, are added to the given problem, what effect will be? (choose all the effects)
a) The feasible solution area will be smaller.
b) The feasible solution area will be larger.
c) The given problem becomes infeasible.
d) The optimal point will be changed.
e) The objective value will be decreased.
f) There will be no effect.
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