Exam 14: Optimization Modeling: Applications

A statistician is currently trying to maximize his profit in the bond market.Four bonds are available for purchase and sale at the bid and ask prices shown in the table below.The statistician can buy up to 1300 units of each bond at the ask price or sell up to 1300 units of each bond at the bid price.During each of the next three years the person who sells a bond will pay the owner of the bond the cash payments that are also shown in the table below.The statistician's goal is to maximize his revenue from selling bonds less his payments for buying bonds,subject to the constraint that after each year's payments are received,his current cash position (due only to cash payments from bonds and not purchases or sales of bonds)is nonnegative.His current cash position can depend on past coupons and that cash accumulated at the end of each year earns 12% annual interest.Determine how to maximize net profit from buying and selling bonds,subject to the constraints previously described.

The market manager is concerned about variability in the fat content of beef,noting that it actually can be as high as 20% and as low as 5%.For the model in Question 117,perform a sensitivity analysis to determine the effect,first on the amount of beef used,and then on the revenue.What do the results indicate? Should the manager be concerned?

During each 4-hour period,the police force in a small town in Ohio requires the following number of on-duty police officers: 8 from midnight to 4 A.M.; 7 from 4 A.M.to 8 A.M.; 6 from 8 A.M.to noon; 6 from noon to 4 P.M.; 5 from 4 P.M.to 8 P.M.; and 4 from 8 P.M.to midnight.Each police officer works two consecutive 4-hour shifts.Determine how to minimize the number of police officers needed to meet the town's daily requirements.

Many organizations must determine how to schedule employees to provide adequate service.If we assume that an organization faces the same situation each week,this is referred to as

During the next 4 quarters,an automobile company must meet (on time)the following demands for cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3; 1000 in quarter 4.At the beginning of quarter 1,there are 300 autos in stock.The company has the capacity to produce at most 3000 cars per quarter.At the beginning of each quarter,the company can change production capacity.It costs $100 to increase quarterly production capacity by 1 unit.For example,it would cost $20,000 to increase capacity from 3000 to 3200.It also costs $60 per quarter to maintain each unit of production capacity (even if it is unused during the current quarter).The variable cost of producing a car is $2200.A holding cost of $160 per car is assessed against each quarter's ending inventory.It is required that at the end of quarter 4,plant capacity must be at least 4000 cars.Determine how to minimize the total cost incurred during the next 4 quarters.

Many organizations must determine how to schedule employees to provide adequate service.If we assume that an organization faces the same situation each week,this is referred to as

Determine how to minimize the transportation cost in meeting the oil demands of Los Angeles and New York.

My friend Lee Meadow moved from Ferris State University in Michigan to Indiana University East in Indiana and has rented a truck that can haul up to 1100 cubic feet of furniture.The volume and value of each item he considered moving on the truck are giving below. Which items did he take with him to Indiana? What is the value of these items?

Which of the following statements are false?

An oil delivery truck contains five compartments,holding up to 2800,2900,1200,1800,and 3200 gallons of fuel,respectively.The company must deliver three types of fuel (super,regular,and unleaded)to a customer.The demands,penalty per gallon short,and the maximum allowed shortage are shown in the table below.Each compartment of the truck can carry only one type of gasoline.Determine how to load the truck in a way that minimizes shortage costs.

Determine the optimal processing plan for the meat market.

In a minimum cost network flow model,the flow balance constraint for each supply node takes the form

Integer programming (IP)models are optimization models in which all of the variables must be integers.

Multiple optimal solutions are quite common in linear programming models.

You have decided to enter the candy business.You are considering producing two types of candies: A and B,both of which consist solely of sugar,nuts,and chocolate.At present you have in stock 12,000 ounces of sugar,3000 ounces of nuts,and 3000 ounces of chocolate.The mixture used to make candy A must contain at least 10% nuts and 10% chocolate.The mixture used to make candy B must contain at least 20% nuts.Each ounce of candy A can be sold for $0.40 and each ounce of candy for $0.50.Determine how you can maximize your revenues from candy sales.

A typical transportation problem requires which of the following sets of input numbers:

When we solve a nonlinear programming problem (NLP),it is very possible that Solver will obtain the wrong answer.

Determine how to minimize the sum of shortage and shipping costs.

A nonlinear programming problem (NLP)is an optimization problem in which the objective function and/or the constraints are not linear functions of the decision variables.

Determine the optimal staffing plan for the project.