Exam 10: Integer Programming, Goal Programming, and Nonlinear Programming

Which of the following is a category of mathematical programming techniques that doesn't assume linearity in the objective function and/or constraints?

Define quadratic programming.

A package express carrier is considering expanding the fleet of aircraft used to transport packages.Of primary importance is that there is a total of $350 million allocated for purchases.Two types of aircraft may be purchased - the C1A and the C1B.The C1A costs $25 million, while the C1B costs $18 million.The C1A can carry 60,000 pounds of packages, while the C1B can only carry 40,000 pounds of packages.Of secondary importance is that the company needs at least 10 new aircraft.It takes 150 hours per month to maintain the C1A, and 100 hours to maintain the C1B.The least level of importance is that there are a total of 1,200 hours of maintenance time available per month. (a)First, formulate this as an integer programming problem to maximize the number of pounds that may be carried. (b)Second, rework the problem differently than in part (a)to suppose the company decides that what is most important to them is that they keep the ratio of C1Bs to C1As in their fleet as close to 1.2 as possible to allow for flexibility in serving their routes.Formulate the goal programming representation of this problem, with the other three goals having priorities P2, P3, and P4, respectively.

Requiring an integer solution to a linear programming problem decreases the size of the feasible region.

In an integer programming problem, if it is desired to have variable X be exactly twice the value of variable Y, the constraint would be written

A capital budgeting problem involving the selection of possible projects under budget constraints is solved by which of the following?

As part of a larger problem, you are trying to determine whether or not to open a plant with a capacity of 10,000 units (using binary variable Y).You also define X as the number of units (if any)produced at that plant.How will you ensure that Y will equal 1 if the plant is open?

Which of the following is not considered nonlinear programming?

In goal programming, the deviational variables have the same objective function coefficients as the surplus and slack variables in a normal linear program.

What is mixed integer programming?

Agile Bikes has manufacturing plants in Salt Lake City, Dallas, and Chicago.The bikes are shipped to retail stores in Los Angeles, New York, Miami, and Seattle.Information on shipping costs, supply, and demand is given in the following table: Where should Los Angeles receive their bicycles from?

Agile Bikes has manufacturing plants in Salt Lake City, Dallas, and Chicago.The bikes are shipped to retail stores in Los Angeles, New York, Miami, and Seattle.Information on shipping costs, supply, and demand is given in the below table.What is the minimum cost solution to this bicycle shipment scenario?

A 0-1 programming representation could be used to assign sections of a course to specific classrooms.

Johnny's apple shop sells homemade apple pies and freshly squeezed apple juice.Each apple pie requires 2 apples, and 1 apple yields 4 ounces of juice.Customers use a self-service dispenser to pour apple juice in a container and are charged by the ounce at a rate of $0.50 per ounce.The contribution to profit of the apple pie, factoring in the apples and remaining ingredients are $2 per pie, and the contribution to profit of freshly squeezed apple juice is $0.20 per ounce.In a given day, there must be at least 100 ounces of apple juice produced and at least 10 apple pies.The company has a supply of 60 apples per day.Formulate this problem as a mixed integer program.Apple pies must be produced in whole quantities, but any positive value is positive for juice production.

When solving very large integer programming problems, we sometimes have to settle for a "good," not necessarily optimal, answer.

A haberdashery produces scarves, ascots, and capes.The profit function for the haberdashery is expressed by the following equation: profit = 4S + 2A + 5C + 0.8S² + 1.4A² + 2C^{2 + 2SAC}.It takes 9 minutes to produce a scarf, 13 minutes to produce an ascot and 30 minutes to produce a cape.There is a total of 50 hours available for labor each week.There must be at least 50 scarves, 100 ascots, and 25 capes produced each week.Formulate a nonlinear program representing the profit maximization problem for the haberdashery and solve using Solver's GRG Nonlinear routine.

The following objective function is nonlinear: Max 5X - 8YZ.

Unfortunately, goal programming, while able to handle multiple objectives, is unable to prioritize these objectives.

The constraint X₁ + X₂ + X₃+ X₄ ≤ 2 with 0 -1 integer programming allows at most two of the items X_1, X_2, X_3, and X₄ to be selected to be a part of the optimal solution.

A haberdashery produces scarves, ascots, and capes.The profit function for the haberdashery is expressed by the following equation: profit = 4S + 2A + 5C + 0.8S² + 1.4A² + 2C² + 2SAC.It takes 10 minutes to produce a scarf, 15 minutes to produce an ascot and 30 minutes to produce a cape.There is a total of 50 hours available for labor each week.There must be at least 50 scarves, 100 ascots, and 25 capes produced each week.Formulate a nonlinear program representing the profit maximization problem for the haberdashery and solve using Solver's GRG Nonlinear routine.