# Question: Consider the following nonconvex programming problem Maximize f x 1 000x

Consider the following nonconvex programming problem:

Maximize f(x) = 1,000x – 400x2 + 40x3 – x4,

Subject to x2 + x ≤ 500 and x ≥ 0.

(a) Identify the feasible values for x. Obtain general expressions for the first three derivatives of f(x). Use this information to help you draw a rough sketch of f(x) over the feasible region for x. Without calculating their values, mark the points on your graph that correspond to local maxima and minima.

(b) Use the bisection method with ϵ = 0.05 to find each of the local maxima. Use your sketch from part (a) to identify appropriate initial bounds for each of these searches. Which of the local maxima is a global maximum?

Maximize f(x) = 1,000x – 400x2 + 40x3 – x4,

Subject to x2 + x ≤ 500 and x ≥ 0.

(a) Identify the feasible values for x. Obtain general expressions for the first three derivatives of f(x). Use this information to help you draw a rough sketch of f(x) over the feasible region for x. Without calculating their values, mark the points on your graph that correspond to local maxima and minima.

(b) Use the bisection method with ϵ = 0.05 to find each of the local maxima. Use your sketch from part (a) to identify appropriate initial bounds for each of these searches. Which of the local maxima is a global maximum?

**View Solution:**## Answer to relevant Questions

Consider the following nonconvex programming problem: Maximize f(x) = 3x1 x2 – 2x21 – x32, Subject to and x1 ≥ 0, x2 ≥ 0. (a) If SUMT were to be applied to this problem, what would be the unconstrained function P(x; ...Because of population growth, the state of Washington has been given an additional seat in the House of Representatives, making a total of 10. The state legislature, which is currently controlled by the Republicans, needs to ...Reconsider the example of a constrained minimum spanning tree problem presented in Sec. 14.2 (see Fig. 14.7(a) for the data before introducing the constraints). Starting with a different initial trial solution, namely, the ...Consider an 8-city traveling salesman problem (cities 1, 2, . . . , 8) where city 1 is the home city and links exist between all pairs of cities. For each of the following pairs of parents, generate their two children when ...Consider the 8-city traveling salesman problem whose links have the associated distances shown in the following table (where a dash indicates the absence of a link).Post your question