Exam 1: Introduction

Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's.

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.

A furniture store has set aside 800 square feet to display its sofas and chairs.Each sofa utilizes 50 sq.ft.and each chair utilizes 30 sq.ft.At least five sofas and at least five chairs are to be displayed. a.Write a mathematical model representing the store's constraints. b.Suppose the profit on sofas is $200 and on chairs is $100.On a given day,the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05.Mathematically model each of the following objectives: 1. Maximize the total pieces of furniture displayed. 2. Maximize the total expected number of daily sales. 3. Maximize the total expected daily profit.

The volume that results in marginal revenue equaling marginal cost is called the break-even point.A8

The decision making process includes implementation and evaluation of the decision.

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

An author has received an advance against royalties of $10,000.The royalty rate is $1.00 for every book sold in the United States,and $1.35 for every book sold outside the United States.Define variables for this problem and write an expression that could be used to calculate the number of books to be sold to cover the advance.

All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.

Identification and definition of a problem

The value of any model is that it enables the user to make inferences about the real situation.

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.

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 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?

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.

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

A manufacturer makes two products,doors and windows.Each must be processed through two work areas.Work area #1 has 60 hours of available production time.Work area #2 has 48 hours of available production time.Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2.Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2.Profit is $8 per door and $6 per window. a.Define decision variables that will tell how many units to build (doors and windows). b.Develop an objective function that will maximize profits. c.Develop production constraints for work area #1 and #2.

A physical model that does not have the same physical appearance as the object being modeled is

The field of management science

Management science and operations research both involve

The quantitative analysis approach requires

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: Monthly fixed cost (loan payment,taxes,insurance,maintenance)$6000 Variable cost per occupied room per night $ 20 Revenue per occupied room per night $ 75 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?