exam 4

Suppose a company sells two different products, x and y, for net profits of $5 per unit and $10 per unit, respectively. The slope of the line representing the objective function is:

. -0.5

Please select the constraints.

. X1A + X1B + X1C + X1D ≤ 1 b. X 3A + X3B + X3C + X3D ≤ 1 c. X1D + X2D + X3D + X4D = 1 d. X1C + X2C + X3C + X4C = 1 e. X2A + X2B + X2C + X2D ≤ 1 f. X4A + X4B + X4C + X4D ≤ 1 g. X1A + X2A + X3A + X4A = 1 h. X1B + X2B + X3B + X4B = 1

The optimal solution to any linear programming model is the:

. corner point of a polygon

The term nonnegativity refers to the condition in which the:

. decision variables cannot be less than zero

When using the graphical solution method to solve linear programming problems, the set of points that satisfy all constraints is called the:

. feasible region

The divisibility property of linear programming means that a solution can have both:

. integer and noninteger levels of an activity

When there is a problem with Solver being able to find a solution, many times it is an indication of a thumbs down

. mistake in the formulation of the problem

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit. This type of problem is referred to as the:

. product mix problem

As related to sensitivity analysis in linear programming, when the profit increases with a unit increase in labor, this change in profit is referred to as the:

. shadow price

In using Excel® to solve linear programming problems, the objective cell represents the:

. value of the objective function

For the upcoming two-week period, machine A has available 80 hours and machine B has available 60 hours of processing time. Forecasts of the markets indicate that the manufacturer can expect to sell a maximum of 16 units of chemical X and 18 units of chemical Y. (D) Identify the optimal production plan. Confirm your solution using Excel Solver. What is the maximized profit?

1350

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available, then an algebraic formulation of this constraint is:

3x+5y<100

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $10000, you will develop the model that will maximize the number reached and achieve an exposure quality if at least 1000. Let T = the number of TV adsLet R = the number of radio adsLet N = the number of newspaper ads (C) Please select the constraints for this decision problem.

500T + 200R + 400N ≤ 10000

If a transportation problem has four origins and five destinations, the LP formulation of the problem will have

9 constraints

Which of the following is not true regarding an LP model of the assignment problem?

All constraints are of the ≥ form.

All decision variables are expressed in thousands of dollars (A) What are the decision variables?

F, G1, G2, S1, S2, S3, S4, S5

Let T = the number of TV adsLet R = the number of radio adsLet N = the number of newspaper ads (B) Please define the objective function.

MAX 10000T+3000R+5000N

All decision variables are expressed in thousands of dollars (B) Please define the objective function

MINIMIZE F

Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is

Min 2M + 3B

Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Give the network model and the linear programming model for this problem.

Min 3XA1 + 2XA2 + 5XA3 + 9XB1 + 10XB2 + 5XC1 + 6XC2 + 4XC3

Let X1A denote whether we assign person 1 to task A. If we assign person 1 to task A, X1A = 1. If we do not assign person 1 to task A, X1A = 0. We similarly define the other variables.

Min 9X1A+5X1B+4X1C+2X1D+12X2A+6X2B+3X2C+5X2D+11X3A+6X3B+5X3C+7X3D

Let T = the number of TV adsLet R = the number of radio adsLet N = the number of newspaper ads (A) What are the decision variables?

T,RN

Which of the following is not true regarding the linear programming formulation of a transportation problem?

The number of constraints is (number of origins) x (number of destinations).

What are the decision variables?

X1B, X2C, X3D b. X1A, X2B, X3C c. X1D, X2D, X3B d. X1C, X2A, X3A

The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means

agent 3 can be assigned to 2 tasks

In an all-integer linear program,

all variables must be integer.

Rounding the solution of an LP Relaxation to the nearest integer values provides

an integer solution that might be neither feasible nor optimal.

All optimization problems have:

an objective function and decision variables

In a transshipment problem, shipments

can occur between any two nodes.

If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a

corequisite constraint.

In using Excel® to solve linear programming problems, the decision variable cells represent the:

decision variables

The difference between the transportation and assignment problems is that

each supply and demand value is 1 in the assignment problem

Rounded solutions to linear programs must be evaluated for

feasibility and optimality.

The solution of a linear programming problem using Excel® typically involves the following three stages: Select one:

formulating the problem, invoking Solver, and sensitivity analysis

The shortest-route problem finds the shortest-route

from the source to any other node.

Media selection problems usually determine

how many times to use each media source

The feasible region in all linear programming problems is bounded by:

hyperplanes

Constraints in a transshipment problem

include a variable for every arc.

The additivity property of linear programming implies that the contribution of any decision variable to the objective is of/on the levels of the other decision variables.

independent

Arcs in a transshipment problem

indicate the direction of the flow.

Every linear programming problem involves optimizing a:

linear function subject to several linear constraints

To study consumer characteristics, attitudes, and preferences, a company would engage in

marketing research.

Linear programming is a subset of a larger class of models called:

mathematical programming models

The objective of the transportation problem is to

minimize the cost of shipping products from several origins to several destinations.

In most cases, when solving linear programming problems, we want the decision variables to be:

nonnegative

In an optimization model, there can only be one:

objective function

The graph of a problem that requires x1 and x2 to be integer has a feasible region

of dots.

In the general linear programming model of the assignment problem,

one agent is assigned to one and only one task.

Most practical applications of integer linear programming involve

only 0-1 integer variables and not ordinary integer variables.

Linear programming models have three important properties:

proportionality, additivity, and divisibility

An efficient algorithm for finding the optimal solution in a linear programming model is the:

simplex method

The parts of a network that represent the origins are

the nodes

The problem which deals with the distribution of goods from several sources to several destinations is the

transportation problem

The assignment problem is a special case of the

transportation problem.

A linear programming problem with _____decision variable(s) can be solved by a graphical solution method.

two

In some cases, a linear programming problem can be formulated such that the objective can become infinitely large (for a maximization problem) or infinitely small (for a minimization problem). This type of problem is said to be:

unbounded

Which of the following is the most useful contribution of integer programming?

using 0-1 variables for modeling flexibility

Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?

x1 + x2 + x3 ≥ 2

In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible?

x1 = 2, x2 = 3, x3 = .578

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y. An algebraic formulation of these constraints is:

x>60, y>80

The number of units shipped from origin i to destination j is represented by

xij.

A mutual fund manager must decide how much money to invest in Atlantic Oil (A) and how much to invest in Pacific Oil (P). At least 60% of the money invested in the two oil companies must be in Pacific Oil. A correct modeling of this constraint is

​-0.6A + 0.4P > 0.

​In a production scheduling LP, the demand requirement constraint for a time period takes the form

​beginning inventory + production - ending inventory = demand

Conditions that must be satisfied in an optimization model are:​

​constraints

​The production scheduling problem modeled in the textbook involves capacity constraints on all of the following types of resources except

​material.

​Assuming W1, W2 and W3 are 0 -1 integer variables, the constraint W1 + W2 + W3 < 1 is often called a

​mutually exclusive constraint.

Which of the following is not a characteristic of assignment problems?​

​the signs of constraints are always <

Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then Select one:

−.5A + .5B − .5C ≤ 0