Operations Research Answers

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

A motor company manufacture and sell cars and motorbikes. The cost of manufacturing x motorbikes and y cars is given by 2 2 C x y x xy y ( , ) 100 100 400 = + + . Each motorbike is sold for N$36 000-00 and each car is sold for N$180 000-00. Use Cramer’s rule to determine the number of motorbikes and the number of cars that should be manufactured and sold for a maximum profit  and determine the maximum profit max . (10 marks) 4.2 Use the Jacobian to test for functional dependence between the cost and the revenue functions in 4.1. (7 marks) 4.3 One of the stationary points of the function ( ) 4 4 2 2 f x y x y x xy y , 2 4 2 = + − + − is ( 2, 2 − ). Use the Hessian to test whether the given point is a maximum, minimum or a saddle point.

As part of a campaign to promote its Summer Annual Clearance Sale, Cassy clothing cc. decided to buy television advertising time on Etu television. Their television advertising budget was N$102 000-00. Morning time costs N$3000-00 per minute, afternoon time costs N$1000-00 per minute, and evening (prime) time costs N$12 000-00 per minute. Because of previous commitments, Etu television could not offer Cassy clothing more than 6 minutes of prime time and a total of 25 minutes of advertising time over the two weeks in which the commercials run in the morning would be seen by 200 000 people, those run in the afternoon would be seen by 100 000 people and those run in the evening would be seen by 600 000 people. How much morning, afternoon, and evening advertising time should Cassy clothing buy to maximize exposure of its products? 

1.      A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18 ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The demand for bracelets is no more than four. A necklace earns $300 in profit and a bracelet, $400. The store wants to determine the number of necklaces and bracelets to make in order to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

As part of a campaign to promote its Summer Annual Clearance Sale, Cassy clothing cc. decided to buy television advertising time on Etu television. Their television advertising budget was N$102 000-00. Morning time costs N$3000-00 per minute, afternoon time costs N$1000-00 per minute, and evening (prime) time costs N$12 000-00 per minute. Because of previous commitments, Etu television could not offer Cassy clothing more than 6 minutes of prime time and a total of 25 minutes of advertising time over the two weeks in which the commercials run in the morning would be seen by 200 000 people, those run in the afternoon would be seen by 100 000 people and those run in the evening would be seen by 600 000 people. How much morning, afternoon, and evening advertising time should Cassy clothing buy to maximize exposure of its products?