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Math 132A Assignment 7

Due: Friday, March 15th at Midnight on Gradescope.

1. (a) Find a minimizer of  subject to 2x1 + x2 = 1.

(b) If the constraint is changed to 2x1 + x2 = 1 + δ for a δ, estimate the change in value of the objective function. Compare this estimate with the actual change in value when δ = 0.25.

2. Let a1, a2, a3 be positive constants. Find a maximizer of the function f(x) = x1x2x3 subject the constraint

3. Find local minimizers of

4. For any vector c ∈ Rn solve the problem

5. Solve

6. Solve

(It may help to graph the feasible region to guess possible minimizers, but be sure to verify your guess(es) using the optimality conditions.)