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d. Construction industry

b. Machining process

C. Oil industry

a. Healthcare

e. Agriculture planning

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Formulate an integer program to find the shortest path from node 1 to 5.

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A)Formulate an LP whose solution will maximize the total happiness, considering x_ij as the fraction of time ih man spends with j™ woman.

b) Solve it with Lingo, did you find an integer solution? What do you think it means?

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Using units of thousands of acre feet, the tables below the diagram show the maximum amount of water that can be pumped through each aqueduct per day.

The city water manager wants to determine a flow plan that will maximize the flow of water to the city.

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a)Draw the network diagram. Write down the LP to determine the completion time. Write down the activities on the critical path.

b)Suppose that by hiring additional workers, the duration of each activity can be reduced. The costs per day of reducing the duration of the activities are given in the following table. Write down the LP to complete the project within 20 days with minimum cost.

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a) Construct the transportation tableau

b) Is this a balanced transportation model? If not, convert it into a balanced model

c) Write the LP formulation for this problem.

d) Solve it with Excel or Lingo, write down the optimal solution on your answer sheet(values of the decision variables and the objective function ). Include your software model and output files