Exam 14: Optimization Models

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

Two common applications of optimization in finance are investment strategy and pension fund management.

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

Determine the optimal staffing plan for this project.

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.

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

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

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

A company produces three types of glue on two different production lines.Each line can be utilized by up to six workers at a time.Workers are paid $550 per week on production line 1 and $950 per week on production line 2.For a week of production,it costs $1,050 to set up production line 1 and $2,050 to set up production line 2.During a week on a production line each worker produces the number of units of glue shown in the table below: Each week at least 120 units of glue 1,at least 150 units of glue 2,and at least 200 units of glue 3 must be produced.What is the minimum total cost that will meet weekly demands?

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

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

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

The project manager is evaluating options to complete the project early so that the company can earn a bonus.He has determined that the project schedule can be compressed into a six-month schedule,with the same total number of worker-months.In that case,the staffing requirements are as shown below. Develop an optimal staffing plan for the project under the accelerated schedule.

Multiple optimal solutions are quite common in linear programming models.

In transportation problem,shipping costs are often nonlinear due to quantity discounts.

The objective in transportation problems is typically to

An oil company controls two oil fields.Field 1 can produce up to 45 million barrels of oil per day,and Field 2 can produce up to 55 million barrels of oil per day.At Field 1,it costs $3 to extract and refine a barrel of oil; at Field 2,the cost is $2.The company sells oil to two countries: France and Japan.The shipping costs per barrel are shown below. Each day,France is willing to buy up to 45 million barrels (at $6 per barrel),and Japan is willing to buy up to 35 million barrels (at $6.50 per barrel).What is the maximum profit the company can make?

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.

In formulating a transportation problem as linear programming model,which of the following statements is not correct?

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.