Consider the following optimization problem: maximize x1,x2 c = x2 1 + 4x2 2 2x1 +
Question:
Consider the following optimization problem:
maximize
x1,x2
c = x2
1 + 4x2
2 − 2x1 + 8x2
subject to x1 + 2x2 ≥ 7.
A. about Slater's condition [5 points]
Does this problem have strong duality? Use Slater's condition for showing it.
Hint: this problem does not have any equality constraint. Therefore, checking the Slater's condition
becomes even easier.
B. about the method of Lagrange multipliers [30 points]
Solve this optimization problem using the method of Lagrange multipliers. Specifically do the following:
• Find its optimal primal variables, optimal dual variable, optimal primal function value, and optimal
dual function value.
• Compare and discuss the optimal primal function value and the optimal dual function value, based
on your answer to Section A.
Financial Accounting an introduction to concepts, methods and uses
ISBN: 978-0324789003
13th Edition
Authors: Clyde P. Stickney, Roman L. Weil, Katherine Schipper, Jennifer Francis