Exam 14: Optimization Models

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.

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.

Rounding the solution of a linear programming problem to the nearest integer values provides a(n):

Transshipment points are locations where goods neither originate nor end up,but goods are allowed to enter such points to be shipped out to their eventual destinations.

In a typical minimum cost network flow model,the nodes indicate

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

If all the supplies and demands for a transportation model are integers,then the optimal Solver solution may or may not have integer-valued shipments.

A problem that deals with the direct distribution of products from supply locations to demand locations is called a(n)_____ problem.

If an LP problem is not correctly formulated,Solver will automatically indicate that it is infeasible when trying to solve it.

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

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.

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.

Which of the following is a type of constraint often required in blending problems?

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

The constraints in a blending problem can be specified in a valid way and still lead to which of the following problems?

In blending problems,if a quality constraint involves a quotient,then the problem will be nonlinear.

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?

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

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

To specify that must be at most 75% of the blend of , ,and ,we must have a constraint of the form