Exam 1: Introduction

Jane Persico, facility engineer at the El Paso plant of Computer Products Corporation (CPC), is studying a process selection decision at the plant. A new printer is to be manufactured and she must decide whether the printer will be auto-assembled or manually assembled. The decision is complicated by the fact that annual production volume is expected to increase by almost 50% over three years. Jane has developed these estimates for two alternatives for the printer assembly process:​ ​ ​ a. Which production process would be the least-cost alternative in Years 1, 2, and 3? b. ​ How much would the variable cost per unit have to be in Year 2 for the auto-assembly process to justify the additional annual fixed cost for the auto-assembly process over the manual assembly process? ​

The most critical component in determining the success or failure of any quantitative approach to decision making is problem definition.

A small firm builds galvanized swing sets. The investment in plant and equipment is $200,000. The variable cost per swing set is $500. The selling price of the swing set is $1000. How many swing sets would have to be sold for the firm to break even?

If you are deciding to buy either machine A, B, or C with the objective of minimizing the sum of labor, material and utility costs, you are dealing with a single-criterion decision.

The first step in the decision making process is to identify the problem.

To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs are estimated as follows. Annual fixed costs to operate the school are $30,000. The annual cost per car is $3000. The annual cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is $350. Let x be the number of cars and y be the number of students. a. Write an expression for total cost. b. Write an expression for total revenue. c. Write an expression for total profit. d. ​ ​ The school offers the course eight times each year. Each time the course is offered, there are two sessions. If they decide to operate five cars, and if four students can be assigned to each car, will they break even?

George Dantzig is important in the history of management science because he developed

To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.

​Explain the relationship between information systems specialists and quantitative analysts in the solution of large mathematical problems.

Should the problem solving process be applied to all problems?

In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume. Give the cell formula for a.cell E12, break-even volume. b.cell E16, total revenue. c.cell E17, total cost. d.cell E19, profit (loss).​

A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is $5.50. a.Define variables that would tell how many units to purchase from each source. b.Develop an objective function that would minimize the total cost. c.The manufacturer needs at least 12000 units of corn. The Iowa cooperative can supply up to 8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints for these conditions.

The first step in problem solving is

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected: ​ a.Write the expression for total cost per month. Assume 30 days per month. b.Write the expression for total revenue per month. c.​If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even?

​What are three of the management science techniques that practitioners use most frequently? How can the effectiveness of these applications be increased?

The relationship d = 5000 − 25p describes what happens to demand (d) as price (p) varies. Here, price can vary between $10 and $50. a.How many units can be sold at the $10 price? How many can be sold at the $50 price? b.Model the expression for total revenue. c.Consider prices of $20, $30, and $40. Which of these three price alternative will maximize total revenue? What are the values for demand and revenue at this price?

Consider a department store that must make weekly shipments of a certain product from two different warehouses to four different stores. a.How could a quantitative approach to decision making be used to solve this problem? b.What would be the uncontrollable inputs for which data must be gathered? c.What would be the decision variables of the mathematical model? the objective function? the constraints? d.Is the model deterministic or stochastic? e.Suggest assumptions that could be made to simplify the model.

In quantitative analysis, the optimal solution is the mathematically-best solution.

​Explain the difference between controllable and uncontrollable inputs to a mathematical model and provide an example of each.

Organizers of an Internet training session will charge participants $150 to attend. It costs $3000 to reserve the room, hire the instructor, bring in the equipment, and advertise. Assume it costs $25 per student for the organizers to provide the course materials. a.How many students would have to attend for the company to break even? b.If the trainers think, realistically, that 20 people will attend, then what price should be charged per person for the organization to break even?