undefined

1. [15 pts.] Five workers are available to perform four jobs. The time it takes each worker to perform each job is given in the following table. The goal is to assign workers to jobs so as to minimize the total time required to perform the four jobs. Use the Hungarian method to solve the problem Time thours) Job 1 Job 2 Job 3 Job 4 Worker 1 10 15 10 15 Worker 2 12 8 20 10 Worker 3 12 9 12 18 Worker 4 6 12 15 18 Workers 16 12 8 12 *_*1*1*1.1 and 1 2. (20 pts. Consider the following transportation table for a minimization problem. Sury Comand a Draw the network diagram (Write the related parameters on nodes and arcs) (2 pts) b Formulate the linear programming model to minimize the total transportation cost. (Write the decision variables, objective function and the constraints ) (6 pts.] Find a basic feasible solution for the given transportation problem using northwest corner method. Write the basic variables and their values clearly 12 pts1 d Find optimal solution by using stepping-stone method. (For each iteration Calculate improvement indices, write loops and total cost) (10 pts) 3. [15 pts | Four projects are available for investment. The projects require the cash flows and yield the net present values (NPV) (in millions) shown in the following table, Project Cash outflow at time NPV d milion Lira) (million Lira) 1 4 5 6 20 million Lira is available for investment at time 0 find the investment plan that maximizes NPV. il investments are required to be 0 or 1 (fractional Investment values are not permitted) a Formulate the mathematical model. (Write the decision variables, objective function and the constraints.) (5 pts b. Find the optimal solution by using Branch and Bound method (Draw the branch and bound tree clearly, write also lower bounds(LB)) (Left branches x=0, right branches x =1) [10 pts.)