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For this discussion topic each student is required to have at least 2 postings: One answering at least one of the questions and a second responding to another student’s posting. Please select a question that has not been answered by the time you post your response. You can select any question to answer once all questions are answered. Please do not copy another student’s posting.

This discussion will close at midnight Sunday, October 28th.

1. Define the decision variables and determine the objective function for the following problem.

Consider the following transportation problem:

To (cost)

From 1 2 3 Supply

_____________________________________________

A $ 6 $9 $M 130

B 12 3 5 70

C 4 8 11 100

Demand 80 110 60

_____________________________________________

Where M indicates a very large number. The objective is to minimize total cost.

2. For the problem given in Question 1, determine all the constraints.

3. For the problem given in Question 1, assume that the following special situations occur. Determine one constraint for each of these special situations. The conditions are independent of one another.

(a) No shipment is possible from origin A to destination 3.

(b) At most 50 units can be shipped from origin C to destination 2.

(c) Destination 1 must receive at least 40 units from origins A and B.

4. Define the decision variables and determine the objective function for the following problem.

A plant has four operators to be assigned to four machines. The time (minutes) required by each worker to produce a product on each machine is shown in the following table:

Machine (min.)

Operator A B C D

_____________________________________________________

1 10 12 9 11

2 5 10 7 8

3 12 14 13 11

4 8 15 11 9

_____________________________________________________

The objective is to minimize total time.

5. For the problem given in Question 4, determine all the constraints.

6. For the problem given in Question 4, assume that the following special situations occur.

Determine one constraint for each of these special situations. The conditions are independent of one another.

(a) Operator 2 cannot be assigned to machine C.

(b) Operator 1 must be assigned to machine A or B.

(c) Machine D can only be operated by operator 3 or 4.

(d) If operator 3 is assigned to machine C then operator 4 must be assigned to machine D but not vice versa.

Notes:

– Answer to Question 1 must be posted before answers to Questions 2 and 3.

– Answer to Question 4 must be posted before answers to Questions 5 and 6.

– Do not find the optimal solution for the two problems.

Use Code GET20