# Question: Consider the following problem Maximize f x x3 2x

Consider the following problem:

Maximize f(x) = x3 + 2x – 2x2 – 0.25x4.

(a) Apply the bisection method to (approximately) solve this problem. Use an error tolerance ϵ = 0.04 and initial bounds x = 0, x-bar = 2.4.

(b) Apply Newton’s method, with ϵ = 0.001 and x1 = 1.2, to this problem.

Maximize f(x) = x3 + 2x – 2x2 – 0.25x4.

(a) Apply the bisection method to (approximately) solve this problem. Use an error tolerance ϵ = 0.04 and initial bounds x = 0, x-bar = 2.4.

(b) Apply Newton’s method, with ϵ = 0.001 and x1 = 1.2, to this problem.

## Answer to relevant Questions

Use the bisection method with an error tolerance ϵ = 0.04 and with the following initial bounds to interactively solve (approximately) each of the following problems. (a) Maximize f(x) = 6x – x2, with x = 0, x-bar = ...Consider the following linearly constrained convex programming problem: Maximize f(x) = 32x1 + 50x2 – 10x22 + x32 – x41 – x42, Subject to and x1 ≥ 0, x2 ≥ 0. Consider the following unconstrained optimization problem: Maximize f(x) = 3x1x2 + 3x2x3 – x21 – 6x22 – x23. (a) Describe how solving this problem can be reduced to solving a two-variable unconstrained optimization ...A stockbroker, Richard Smith, has just received a call from his most important client, Ann Hardy. Ann has $50,000 to invest and wants to use it to purchase two stocks. Stock 1 is a solid blue-chip security with a respectable ...Reconsider the model given in Prob. 13.2-10. What are the KKT conditions for this problem? Use these conditions to determine whether (x1, x2) = (1, 1) can be optimal.Post your question