Exam 14: Optimization Modeling: Applications

Suppose that the company can purchase and ship extra units to either warehouse for a total cost of $125 per unit and that all customer demand must be met.Determine how to minimize the sum of purchasing and shipping costs.

Workforce scheduling problems are often integer programming models,which means that they have:

A manufacturer can sell product 1 at a profit of $2 per unit and product 2 at a profit of $6 per unit.Three units of raw material are needed to manufacture one unit of product 1,and 6 units of raw material are needed to manufacture unit of product 2.A total of 120 units of raw material are available.If any of product 1 is produced,a setup cost of $10 is incurred,and if any of product 2 is produced,a setup cost of $20 is incurred.Determine how to maximize the manufacturer's profit.

Suppose that on Monday morning you have $5000 in cash on hand.For the following seven days,the following cash requirements must be met: Monday,$6,000; Tuesday,$7,000; Wednesday,$10,000; Thursday,$3,000; Friday,$8,000; Saturday,$3,000; Sunday,$4,000.At the beginning of each day,you must decide how much money (if any)to withdraw from the bank.It costs $8 to make a withdrawal of any size.You believe that the opportunity cost of having $1 of cash on hand for a year is $0.25.Assume that opportunity costs are incurred on each day's ending balance.Determine how much money you should withdraw from the bank during each of the next 7 days.

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

A good shipping plan uses as many cheap routes as possible,but ultimately is constrained by capacities and demands.

In formulating a transportation problem as linear programming model,which of the following statements are correct?

The problem which deals with the direct distribution of products from supply locations to demand locations is called a(n)

Chemical Bank is attempting to determine where its assets should be invested during the current year.At present,$800,000 is available for investment in bonds,home loans,auto loans,and personal loans.The annual rate of return on each type of investment is known to be the following: bonds,12%,home loans,18%,auto loans,15%,personal loans,22%.To ensure that the banks portfolio is not too risky,the bank's investment manager has placed the following restrictions on the bank portfolio: -No more than 30% of the total amount invested may be in personal loans -The amount invested in home loans cannot exceed the amount invested in auto loans -The amount invested in personal loans cannot exceed the amount invested in bonds. Determine how the bank can maximize the annual return on its investment portfolio.

Suppose the bonus for completing the project three months early is $250,000.What would be the net bonus to the company,after adjusting for any difference in personnel costs under the accelerated schedule?

You are given the following means,standard deviations,and correlations for the annual return on three stocks.The means are 0.12,0.15,and 0.20.The standard deviations are 0.20,0.30,and 0.40.The correlation between stocks 1 and 2 is 0.65,between stocks 1 and 3 is 0.75,and between stocks 2 and 3 is 0.41.You have $13,000 to invest and can invest no more than half of your money in any single stock.Determine the minimum variance portfolio that yields an expected annual return of at least 0.14.

Which of the following is not a required input for a typical transportation problem?

Aggregate planning models are usually implemented through a rolling planning horizon.

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

A large accounting firm has three auditors.Each can work up to 180 hours during the next month,during which time three projects must be completed.Project 1 takes 140 hours,project 2 takes 150 hours,and project 3 takes 170 hours.The amount per hour that can be billed for assigning each auditor to each project is given in the table below: Determine how to maximize total billings during the next month by formulating the company's problem as a transportation model.

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

If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by increasing the tolerance setting.

Many of the most successful applications of optimization in the real world have been in the areas of scheduling,blending,logistics and aggregate planning.

Solver may be unable to solve some integer programming problems,even when they have an optimal solution.

The binary variables in the fixed cost models correspond to: