APPLICATION. The questions below possess the highest level of assessment of your understanding of the principles. Answer the following as instructed and make your answers concise. Solutions are required. Use clean bond paper for your answers/solutions. Take a picture of your solutions afterwards and turn-in here. Consider the following LP maximization problem. Max 30x1 + x2 s.t. 2x1 + x2 ≤ 4 2x1 + 2x2 ≤ 6 x1, x2 ≥ 0 (a) Solve graphically and state the optimal solution.
- APPLICATION. The questions below possess the highest level of assessment of your understanding
of the principles. Answer the following as instructed and make your answers concise. Solutions are
required. Use clean bond paper for your answers/solutions. Take a picture of your solutions
afterwards and turn-in here.
Consider the following LP maximization problem.
Max 30x1 + x2
s.t.
2x1 + x2 ≤ 4
2x1 + 2x2 ≤ 6
x1, x2 ≥ 0
(a) Solve graphically and state the optimal solution.
(b) Keeping all the other data as is, what per unit profitability should the product, whose current optimal value is zero, have in order that this product enter the optimal solution at a positive level?
(c) How many optimal corner solutions exist after making the change described in part (b)? What are they?
(d) In the original problem, how much can the right-hand side (RHS) of the second constraint be increased (or decreased) before the optimal solution is changed?
(e) Answer part (d) for the RHS of the first constraint.
(f) How do you explain the difference between parts (d) and (e)?
(g) What will be the impact of adding the constraint 4x1 + x2 = 4 to the original model?
(h) What is the impact (on the optimal solution) of adding the constraint 3x1 + 3x2 ≤ 15 to the original
model?
(i) Fill in the blanks:
The difference between parts (g) and (h) is that the original optimal solution already
_______ the constraint in (h) but does not _______ the constraint in (g).
(j) Solve this LP problem using the Simplex method but change the objective function to Max 30x1 + 20x2 but retain the constraints. Then give the optimal solution and objective function value. You need not answer (b) – (i).
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