Operations research UE Past Papers Questions.

The duality theory in linear programming is essentially a unifying theory that develops the relationships between a given linear program and another related linear program stated in terms of variables with the shadow-price interpretation. However, the management scientists have equated the Lagrange multiplier () in the Non-Linear programming to shadow price in the linear programming. Use the following non-linear programming model to show that the Lagrange Multiplier, , is equivalent to the shadow price of the resource.

Maximize

Subject to

labour hours

Where = number of bowls and = number of mugs.

Answer / Solution

UNSOLVED

The basic simplex solutions of typical maximization and minimization linear programming problems have been found to be one of the best methods. However, there are several special types of atypical linear programming problems. Although these special cases do not occur frequently, they can be described within the framework of simplex so that anyone can recognize them when they arise. Mention ANY TWO of these special cases and explain how they can be described in the basic simplex framework.

Answer / Solution

UNSOLVED

Use the following linear programming problem modeled in Microsoft Excel.

1. Write the formula for cells C13, E8 and H7.
2. Explain the economical meaning of “0” in cell H8.

Answer / Solution

UNSOLVED

Briefly outline the steps of the scientific method for attacking problems

Answer / Solution

UNSOLVED

Kathleen Allen, an individual investor, has $70,000 to divide among several investments. The alternative investments are municipal bonds with an 8.5% annual return, certificates of deposit (CDs) with a 5% return, treasury bills with a 6.5% return, and a growth stock fund with a 13% annual return. The investments are all evaluated after one year. However, each investments alternative has a different perveived risk to investor; thus it is advisable to diversify. Kathleen wants to know how much to invest in each alternative in order to maximize the return.

The following guidelines have been established for diversifying the investments and lessening the risk perceived by the investor:

1. No more than 20% of the total should be in municipal bonds
2. The amount invested in certificates of deposits should not exceed the amount invested in the other three alternatives
3. At least 30% of the investment should be in treasury bills and certificates of deposit.
4. To be safe, more should be invested in CDs and treasury bills than in municipal bonds and the growth stock fund, by a ratio of at least 1.2 to 1.

Kathleen wants to invest the entire $70,000. Formulate the linear programming model for this problem so as to maximize the total return from the investment.

Answer / Solution

UNSOLVED