Operations Research Answers

Solve the following job sequencing problem by giving an optimal sequence of jobs, and find the

total elapsed time also. Note that M1, M2, M3, M4, M5 and M6 are machines and A, B, C, D

are jobs.

Jobs → A B C D

M1 20 19 13 22

M2 10 8 7 6

M3 9 11 10 5

Machines M4 4 8 7 6

M5 12 10 9 10

M6 27 21 17 14

Solve the following job sequencing problem by giving an optimal sequence of jobs, and find the

total elapsed time also. Note that M1, M2, M3, M4, M5 and M6 are machines and A, B, C, D

are jobs.

Jobs → A B C D

M1 20 19 13 22

M2 10 8 7 6

M3 9 11 10 5

Machines M4 4 8 7 6

M5 12 10 9 10

M6 27 21 17 14

onsider the following problem

Maximize          Z = 6x1+8x2

Subject to: 

                  5x1+2x2 ≤ 20

                  X1+2x2≤ 10

And

                 X1≥ 0, X2≥ 0

a. Construct the dual problem for this primal problem

b. Solve both the primal problem and the dual problem graphically. Identify the CPF solutions and corner-point infeasible solutions for both problems. Calculate the objective function values for all these solutions

c. Use the information obtained in part (b) to construct a table listing the complementary basic solutions for these problems.

d. Work through the simplex method step by step to solve the primal problem. After each iteration (including iteration 0), identify the BF solution for this problem and the complementary basic solution for the dual problem. Also identify the corresponding corner-point solutions.

Consider the following problem

Maximize                   Z = 6_x1+8_x2

Subject to:

                                  5_x1+2_x2 ≤ 20

                                  X₁+2_x2≤ 10

And

                                 X_1≥ 0, X₂≥ 0

An investor wants to identify how much to invest in two funds, one equity and one debt. Total amount available is Rs. 5, 00, 000. Not more than Rs. 3, 00, 000 should be invested in a single fund. Returns expected are 30% in equity and 8% in debt. Minimum return on total investment should be 15%. Formulate as LPP.

An electronics manufacturing company has three production plants, each of which produces three different models of a particular MP3 player. The daily capacities (in thousands of units) of the three plants are shown in the table. Basic model Gold model Platinum model Plant 1 8 4 8 Plant 2 6 6 3 TUTORIAL LETTER SEMESTER 2/2021 MATHEMATICS FOR ECONOMISTS 1B MFE512S 12 Plant 3 12 4 8 The total demands are 300,000 units of the Basic model, 172,000 units of the Gold model, and 249,500 units of the Platinum model. The daily operating costs are $50,000 for plant 1, $60,000 for plant 2, and $60,000 for plant 3. How many days should each plant be operated in order to fill the total demand while keeping the operating cost at a minimum? What is the minimum cost? Use the method of the dual