{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math171A_hw1_sol

# math171A_hw1_sol - Math 171A Homework 1 Solutions...

This preview shows pages 1–2. Sign up to view the full content.

Math 171A Homework 1 Solutions Instructor: Jiawang Nie January 24, 2012 1. Find the optimal solution to the following LP maximize x 1 + 4 x 2 + 3 x 3 subject to 2 x 1 + x 2 + x 3 4 x 1 - x 3 = 1 x 2 0 , x 3 0 . Solution: The second equality constraint x 1 = x 3 + 1 allows us to convert the problem into a two dimensional optimization problem in the variables x 2 and x 3 . Bring it into the problem, we get the following equivalent problem: max 4( x 2 + x 3 ) + 1 , s.t. x 2 + 3 x 3 2 , x 2 0 , x 3 0 . In this problem, there are two variables x 2 and x 3 , we draw a Figure and find the feasible region, see Figure 1. There are three corner points (0 , 0) , (0 , 2 3 ) , (2 , 0). Calculate the objective function value at these three corner points, we get the maximum function value at the point (2 , 0) with a value of 9, then x 1 = x 3 +1 = 1, i.e. the optimal solution of the original problem is x * = (1 , 2 , 0). Use Matlab to check the solution, the optimal solution x * = [1 2 0], which is the same as above. The matlab code as follows: f= [-1; -4; -3]; A = [2 1 1; 0 -1 0; 0 0 -1]; b = [4; 0; 0]; Aeq = [1 0 -1]; beq = 1; x = linprog(f,A,b,Aeq,beq) 2. Draw the feasible region defined by the following six constraints: x 1 + 2 x 2 6 , x 1 - x 2 2 , x 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

math171A_hw1_sol - Math 171A Homework 1 Solutions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online