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

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A \$ 6 \$9 \$M 130

B 12 3 5 70

C 4 8 11 100

Demand 80 110 60

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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

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1 10 12 9 11

2 5 10 7 8

3 12 14 13 11

4 8 15 11 9

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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.

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