Operations research questions.

Define the following terminologies as used in Operations Research.

1. Variable
2. Break -Even point
3. Data
4. Sensitivity analysis

A vending machine at City Airport dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed). Determine the average length of the waiting line and the average time a customer must wait.

By using a vivid example and illustrative diagram, explain the concept of Costs trade offs associated with improved services in an agribusiness firm.

Distinguish (with vivid examples) between transportation and assignment problem.

In 2017 the Tanzania Bureau of Standards (TBS) and the Tropical Pesticides Research Institute (TPRI) had to formulate a team of four officials to do emergency inspection on agribusiness products in four regions of Tanzania. The two organizations together wanted to assign four teams of officials to the four regions in a way that willl minimize the total distance travelled by the officials. The supply is always one team of officials, and the demand is for one team of officials at each game. The distances in kilometre for each team of officals to each game location are shown in the table below.

1. Formulate the linear programming model for this problem
2. Solve this assignment problem by using the opportunity cost operations.

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.

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.

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.

Briefly outline the steps of the scientific method for attacking problems

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.