# Tutorial 5 - earned from each litre of drink is shown...

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

NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA3252 Linear and Network Optimization Tutorial 5 1. Consider a minimization linear programming problem in standard form. Let x be a basic feasible solution associated with the basis B . Prove the following: (a) If the reduced cost of every nonbasic variable is positive, then x is the unique optimal solution. (b) If x is the unique optimal solution and is nondegenerate, then the reduced cost of every nonbasic variable is positive. 2. The following is a simplex tableau of a minimization LP problem. Basic x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 Solution ¯ c 0 - 5 0 4 - 1 - 10 0 0 620 x 8 0 3 0 - 2 - 3 - 1 5 1 12 x 3 0 2 1 3 1 0 3 0 6 x 1 1 - 1 0 0 6 - 4 0 0 0 Determine the leaving variable and the resulting increase or decrease in the cost if the entering variable is (a) x 2 , (b) x 4 , (c) x 5 , (d) x 6 , (e) x 7 . 3. Fatimah’s drink stall sells three types of drink daily. Each type of drink is made from milk and rose syrup. Sixty litres of milk and twenty ﬁve litres of rose syrup are available daily. The composition of each type of drink per litre and the proﬁt

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.

Unformatted text preview: earned from each litre of drink is shown below: Drink Amount of milk Amount of rose syrup Proﬁt Type (litre) (litre) (\$) 1 0.7 0.3 0.7 2 0.8 0.2 0.5 3 0.9 0.1 0.4 Past experience indicates that the total amount of drink of Type 1 and Type 2 sold is not more than the total amount of drink of Type 3 sold. Formulate an LP problem that will maximize proﬁt and ﬁnd the optimal solution using the simplex method. 1 4. Consider the following LP problem (P): max 3 x 1 + 2 x 2 + 3 x 3 s.t. 2 x 1 + x 2 + x 3 = 2-x 1-4 x 2-2 x 3 ≤ -6 x i ≥ ,i = 1 , 2 , 3 . (a) Add artiﬁcial variables where necessary, and write down the auxiliary problem for Phase 1 of the 2-phase method. (b) Solve the auxiliary problem in (a) and determine a basic feasible solution for the given LP problem (P). (c) Proceed to Phase 2 to solve the given LP problem (P). 2...
View Full Document

## This note was uploaded on 12/02/2011 for the course MATH 3252 taught by Professor Tanbanpin during the Spring '10 term at National University of Singapore.

### Page1 / 2

Tutorial 5 - earned from each litre of drink is shown...

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

View Full Document
Ask a homework question - tutors are online