Exam 14: Optimization Modeling: Applications

An auto company must meet (on time)the following demands for cars: 5000 in quarter 1; 3000 in quarter 2; 6000 in quarter 3; 2000 in quarter 4.At the beginning of quarter 1,there are 500 autos in stock.The company has the capacity to produce at most 3600 cars per quarter.At the beginning of each quarter,the company can change production capacity.It costs $125 to increase quarterly production capacity by one unit.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 $2400.A holding cost of $200 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 5000 cars.Determine how to minimize the total cost incurred during the next four quarters.

A global optimal solution is not necessarily the best solution overall.

A local optimal solution is better than all nearby solutions,but a solution far away might be better than it.

A product can be produced on four different machines.Each machine has a fixed setup cost,variable production cost per unit processed,and a production capacity,as shown below: A total of 2000 units of the product must be produced.Determine how to minimize the total cost.

A company blends silicon and nitrogen to produce two types of fertilizers.Fertilizer 1 must be at least 40% nitrogen and sells for $75 per pound.Fertilizer 2 must be at least 70% silicon and sells for $45 per pound.The company can purchase up to 9000 pounds of nitrogen at $16 per pound and up to 12,000 pounds of silicon at $12 per pound.Assuming that all fertilizer produced can be sold,determine how the company can maximize its profit.

(A)Determine how to minimize the total (production plus distribution)costs of meeting the company's annual demand. (B)How would you modify the model in (A)if at most 300 units can be shipped through Chicago?

Assume that you are given the following means,standard deviations,and correlations for the annual return on three stocks. The correlation between stocks 1 and 2 is 0.62,between stocks 1 and 3 is 0.72,and between stocks 2 and 3 is 0.39.You have $12,000 to invest and can invest no more than 55% of your money in any single stock.Determine the minimum variance portfolio that yields an expected annual return of at least 0.15

A minimum cost network flow model (MCNFM)has the following advantage relative to the special case of a simple transportation model:

In network models of transportation problems,arcs represent the routes for getting a product from one node to another.

Any integer programming problem involving 0-1 variables with only one constraint is called a knapsack problem.

Suppose that later in the year,venison will be out of season,but the market will be able to obtain an additional 300 pounds of pork for the same costs.Develop a processing plan in that case.How does the solution change?

The production manager believes the cost of the contract employees,who are currently in high demand,could be somewhat higher - perhaps as high as $10,000 per month.For the model in Question 113,perform a sensitivity analysis to determine the effect on the number of full-time employees that will be needed for the project.

In a set-covering model,each member of a given set (set 1)must be "covered" by an acceptable member of another set (set 2).The objective of such problems is to minimize the number of elements in set 2 that are needed to cover all the elements in set 1.

Transportation and transshipment problems are both considered special cases of a class of linear programming problems called

Laila,an Egyptian Broker,is currently trying to maximize her profit in the bond market.Four bonds are available for purchase and sale at the bid and ask prices shown in the table be below: Laila can buy up to 1000 units of each bond at the ask price or sell up to 1000 units of each bond at the bid price.During each of the next 3 years,the person who sells a bond will pay the owner of the bond the cash payments shown in the table below: Laila's goal is to maximize her revenue from selling bonds less her payment for buying bonds,subject to the constraint that after each year's payments are received,her current cash position (due only to cash payments from bonds and not purchases or sales of bonds)is nonnegative.Note that her current cash position can depend on past coupons and that cash accumulated at the end of each year earns 13% annual interest.Determine how to maximize net profit from buying and selling bonds,subject to the constraints previously described.Why do you think we limit the number of units of each bond that can be bought or sold?

Logistics problems are problems of finding the least expensive way to transport products from their origin to their destination.

At time 0,you have $10,000.Investments A and B are available; their cash flows are shown in the table below: Assume that any money not invested in A or B earns interest at an annual rate of 8%.Determine how to maximize your cash on hand at time 3.

The flows in a general minimum cost network flow model (MCNFM)do all necessarily have to be from "left to right"; that is,from supply points to demand points.

A company manufactures two products.If it charges price for product I,it can sell units of product I,where and .It costs $25 to produce a unit of product 1 and $72 to produce a unit of product 2.How many units of each product should the company produce,and what prices should it charge,to maximize its profit?

The financial CEO is given a group of possible investments projects for his company's capital.For each project,he is given the NPV that each project would add to the firm,as well as the cash outflow required by each project during each year as shown in the table below: Determine the investments that maximize the firm's NPV.The firm has 30 million dollars available during each of the next 5 years.All numbers are in millions of dollars.