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.