Exam 2: Introduction to Optimization and Linear Programming

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X₁ = number of product 1 produced in each batch X₂ = number of product 2 produced in each batch How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Which of the following is the general format of an objective function?

The second step in formulating a linear programming problem is

Retail companies try to find

Solve the following LP problem graphically using level curves.

When do alternate optimal solutions occur in LP models?

A company uses 4 pounds of resource 1 to make each unit of X₁ and 3 pounds of resource 1 to make each unit of X₂. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between X₁, X₂ and resource 1?

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X₁ = number of product 1 produced in each batch X₂ = number of product 2 produced in each batch How many units of resource 1 are consumed by each unit of product 1 produced?

A manager has only 200 tons of plastic for his company. This is an example of a(n)

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X₁ = number of product 1 produced in each batch X₂ = number of product 2 produced in each batch How much profit is earned per each unit of product 2 produced?

The symbols X₁, Z₁, Dog are all examples of

Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they do not change their mind. The investment plans offered are: Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments. Formulate the LP model for this problem.

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

A production optimization problem has 4 decision variables and a requirement that at least b₁ units of material 1 are consumed. Which of the following constraints reflects this fact?

Solve the following LP problem graphically using level curves.

A production optimization problem has 4 decision variables and resource 1 limits how many of the 4 products can be produced. Which of the following constraints reflects this fact?

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I). Which set of points on this diagram defines the feasible solution space?

Why do we study the graphical method of solving LP problems?

The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces a limited demand. There are a limited number of wiring, assembly and inspection hours available next month. The data for this problem is summarized in the following table. a.Formulate the LP model for this problem. b.Solve the problem using the graphical method.

Most individuals manage their individual retirement accounts (IRAs) so they