Consider the following optimization problem Minimize 3x1+8x2 s.t. 2x1+6x2 > 6 x1+2x2 > 2.5 x1+3x2 > 0.5 x1>0 x2>0 a) Graph the feasible region of this linear program. Is the feasible region bounded? Why? (you may use an online tool like desmos.com/calculator) b) Are any of the above constraints redundant? If so, indicate which one(s). Explain why. c) Solve the linear program using the graphical method. Explain your approach.
Answer the given question with a proper explanation and step-by-step solution.
Consider the following optimization problem
Minimize 3x1+8x2
s.t.
2x1+6x2 > 6
x1+2x2 > 2.5
x1+3x2 > 0.5
x1>0 x2>0
a) Graph the feasible region of this linear program. Is the feasible region bounded?
Why? (you may use an online tool like desmos.com/calculator)
b) Are any of the above constraints redundant? If so, indicate which one(s). Explain
why.
c) Solve the linear program using the graphical method. Explain your approach.
d) Consider the feasible region drawn in Part (a) and answer the following: If we add
the constraint 3x1+x2> a (hint: you may use desmos.com/calculator and shift the
parameter a to see how the feasible region changes)
i. For what values of a is this a redundant constraint, if any? Why?
ii. For what values of a is the above optimal solution no longer optimal, if
any? Why?
iii. For what values of a does the problem become infeasible, if any? Why?
e) Consider the original formulation (without the added constraint). We will replace
the original objective function 3 x1+8x2 with 3x1+b x2. For what values of b, will
there be alternative optima (hint: recall that to get alternative optima the objective
function line coincides with one of the constraints)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
