480 words - 2 pages

MIS 208 SPRING 2015

HOMEWORK 1

(due 13:15 on Monday, 6 April 2015, in class at 101)

Reading Assignment: Please read section Duality and Sensitivity Analysis of the text book

Winston. You will be responsible on that section in the exam.

Question 1: Two different products, P1 and P2 can be manufactured by one or both of two different

machines, M1 and M2. The unit processing time of either product on either machine is the same.

The daily capacity of machine M1 is 200 units (of either P1 or P2, or a mixture of both) and the

daily capacity of machine M2 is 250 units. The shop supervisor wants to balance the production

schedule of the two machines such that the total number of units produced on one ...view middle of the document...

a) Formulate the problem as a linear program and find the optimal solution by using appropriate

Simplex Methods that you have seen in the class

b) From the optimum solution determine the status of each resource.

Question 3: The following tableau represents a specific simplex iteration. All variables are

nonnegative. The tableau is not optimal for either a maximization or a minimization problem. Thus,

when a non-basic variable enters the solution it can either increase or decrease z or leave it

unchanged, depending on the parameters of the entering non-basic variable.

(a) Categorize the variables as basic and non-basic and provide the current values of all the

variables.

(b) Assuming that the problem is of the maximization type, identify the non-basic variables

that have the potential to improve the value of z. If each such variable enters the basic

solution, determine the associated leaving variable, if any, and the associated change in z.

Do not use the Gauss-Jordan row operations.

(c) Repeat part (b) assuming that the problem is of the minimization type.

(d) Which non-basic variable(s) will not cause a change in the value of z when selected to

enter the solution?

Question 4:

Solve the problem using graphical method. Clearly indicate the iso-profit lines and the improving

direction. Compute an optimal solution and the optimal value.

Question 5:

Question 6:

Question 7: Find the dual of the following LP.

Question 8: Consider the following LP.

Graphically solve the dual of this LP. Then use complementary slackness to solve the max problem.

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