Exam 6: Integer, Goal, and Nonlinear Programming Models

Use this information for the following questions. Six products are currently waiting processing on a single machine.The machine is available today for a maximum of 25 hours.The processing time per hour for each product along with the profit contribution per product is show below. Product Profit Contribution Processing Time (Hours) A \ 55 5 B \ 70 4 C \ 45 6 D \ 60 5 E \ 50 3 F \ 65 6 -Refer to the information above.Which products should be processed to maximize the total profit contribution?

Consider a model with 3 ranked goals.Solving this model requires us to solve:

If a company produces product A then it must also produce either product B or product C.Which of the following constraints enforces this condition?

A marketing manager is considering the following advertising media to promote a new product. The marketing manager has established the following goals and weights: Goal 1: Reach at least 500,000 individuals;Weight 40. Goal 2: Limit the total spending to $150,000;Weight 60. Formulate and solve this goal programming problem.

In goal programming,the objective is typically to maximize the sum of the deviational variables.

These are problems in which all decision variables must have integer solutions:

Nonlinear programming models can be approximated by linear or almost linear models through a procedure known as ________.

If overachievement is acceptable,the appropriate di⁺ variable can be dropped from the objective function.

Use this information for the following questions. Six products are currently waiting processing on a single machine.The machine is available today for a maximum of 25 hours.The processing time per hour for each product along with the profit contribution per product is show below. Product Profit Contribution Processing Time (Hours) A \ 55 5 B \ 70 4 C \ 45 6 D \ 60 5 E \ 50 3 F \ 65 6 -Refer to the information above.Assume that the following conditions must be met: a)We want to ensure that exactly one of these products: A,B,or C must be processed. b)We want to ensure that if product E is processed then product F must be processed. Which products should be processed to maximize the total profit contribution?

These are problems in which some,but not all,the decision variables must have integer solutions:

An NLP model can have both local and global optimal solutions.

Set up and solve the following nonlinear programming problem using Excel: Max :+ Subject to \leq15 \leq15 +\geq10 ,\geq0

The optimal solution of to an NLP model must be a corner point of the feasible region.

In mixed IP problems,some,but not all,of the decision variables have integer solutions.

Set up and solve the following nonlinear programming problem using Excel: Max: 10+15+5+23 Subject to ++\leq50 2+3\leq150 ,,\geq0

A company incurs a cost that is directly proportional to the magnitude of the decision variable.This is an example of a:

Rounding off the solution to an LP relaxed problem may yield:

A developer wishes to expand an office complex and needs to determine how many small,medium,and large offices to include in the expansion.Each small office requires 400 square feet,each medium office requires 700 square feet,and each large office requires 1200 square feet.The current square footage available for expansion is 35,000 square feet.The developer expects to pay $10,000 for each small office,$20,000 for each medium office,and $35,000 for each large office.The developer wishes to limit his expenditures to $500,000.How many of each type of office should be built if the following goals,stated in no particular order,must be met? Goal 1: The expansion should include approximately 6 small offices. Goal 2: The expansion should include approximately 11 medium offices. Goal 3: The expansion should include approximately 15 large offices. Goal 4: The expansion should consist of approximately 35,000 square feet. Goal 5: The expansion should cost approximately $500,000.

Suppose that XA equals 10.What are the values for d₁⁺ and d₁⁻ in the following constraint? XA + d₁⁻- d₁⁺ = 7

Use this information to answer the following questions. A decision maker is provided with 5 different potential projects and must determine which projects to choose.The projects require different amounts of capital and different expected net present values (NPV)over the next three years. -Refer to the information above.Determine which set of projects should be selected in order to achieve the maximum net present value if the following two conditions must also be met: a)If project 1 is selected,then project 2 must be selected,and vice versa. b)Since projects 4 and 5 require outsourcing various operations,the decision maker wants at most one of these projects to be included in the solution and not both.