Exam 14: Optimization Modeling: Applications

A pharmaceutical company produces a drug from four chemicals.Today the company must produce 1000 pounds of the drug.The three active ingredients in the drug are labeled A,B,and C.By weight,at least 8% of the drug must consist of A,at least 4% must consist of B,and at least 2% must consist of C.The cost per pound of each chemical and the amount of each active ingredient in 1 pound of each chemical are given below.It is necessary that at least 100 pounds of chemical 2 be used. Determine the cheapest way of producing today's batch of this drug.

In aggregate planning models,which of the following statements are correct?

The optimal solution to an LP problem was 3.69 and 1.21.If and were restricted to be integers,then 4 and 1 will be a feasible solution,but not necessarily an optimal solution to the IP problem.

A company is considering investing a total amount of $2.50 million in four bonds.The expected annual return,the worst-case annual return on each bond,and the "duration" of each bond are given in the table below. The duration of a bond is a measure of the bond's sensitively to interest rates.The company wants to maximize the expected return from its bond investments,subject to the following constraints: -The worst-case return of the bond portfolio must be at least 90%. -The average duration of the portfolio must be at most 7 -Because of diversification requirements,at most 35% of the total amount invested in a single bond. Determine how the company can maximize the expected return on its investment.

(A)Determine how to minimize the total cost of meeting all demands. (B)If each refinery had a capacity of 380,000 barrels per day,how would you modify the model in (A)?

In a network representation of a transportation problem,the arcs generally represent:

In aggregate planning models,the number of workers available influences the possible production levels.

A 0-1 variable,also called a binary variable,is a variable that must equal 0 or 1.

When we solve a linear programming problem with Solver,we cannot guarantee that the solution obtained is an optimal solution.

If refers to the number of hours employee works in week ,then to indicate that the number of working hours of 4 employees in week 3 should not exceed 160 hours,we must have a constraint of the form

In nonlinear models,which of the following statements are correct?

The risk index of an investment can be obtained by taking the absolute values of percentage changes in the value of the investment for each year and averaging them.Suppose you are trying to determine what percentage of your money you should invest in T-bills,gold,and stocks.The table below lists the annual returns (percentage changes in value)for these investments for the years 1968-1988. Let the risk index of a portfolio be the weighted average of the risk indexes of these investments,where the weights are the fractions of your money assigned to the investments.Suppose that the amount of each investment must be between 20% and 50% of the total invested.You would like the risk index of your portfolio to equal 0.15,and your goal is to maximize the expected return on your portfolio.Determine the maximum expected return on your portfolio,subject to the stated constraints.Use the average return earned by each investment during the years 1968-1988 as your estimate of expected return.

(A)Assume that before being shipped to Los Angeles or New York,all oil produced at the wells must be refined at either Mobile or Galveston.To refine 10000 barrels of oil costs $12 at Mobile and $10 at Galveston.Assuming that both Mobile and Galveston have infinite refinery capacity,determine how to minimize the daily cost of transporting and refining the oil requirements of Los Angeles and New York. (B)Rework (A)under the assumption that Galveston has a refinery capacity of 150,000 barrels per day,and Mobile has a refinery capacity of 180,000 barrels per day.

A total of 160 hours of labor are available each week at $15 per hour.Additional labor can be purchased at $25 per hour.Capital can be purchased in unlimited quantities at a cost of $45 per unit.If K units of capital and L units of labor are available during a week,then machines can be produced.Each machine sells for $270.How can the firm maximize its weekly profit?

The flow balance constraint for each transshipment node,in a minimum cost network flow model,takes the form

What happens to the revenue when the optimal plan changes to the one given in Question 118?

The LP relaxation of an integer programming (IP)problem is the same model as the IP model except that some integer constraints are omitted.

The decision variables in transportation problems are:

A company has daily staffing requirements for two types of jobs,cleaning and customer service persons.The minimum numbers of workers required each day for each type of job are shown in the table below.To meet these requirements,the company can employ three types of workers: those who clean only,those who can perform customer service only,and those who are able to do both.In each of these three categories,the company wants to meet its daily requirements using only full-time workers.A full-time worker must work five consecutive days with two days off.Workers who are able to perform only one type of work (cleaning or customer service)earn $50 per day.Those who are able to perform both types of work earn $60 per day.As a matter of policy,the company wants to ensure that at least 20% of its total hours are staffed by "swing workers"; those who can do both types of jobs.The company wants to find a staffing policy that covers the daily worker requirements at minimum total costs per week.Use solver to formulate and solve the company's problem.

For some types of integer programming problems,their LP relaxation solutions are optimal.