Question 1

The optimal solution in a linear programming problem _____.

Accepted Answer

A) is determined by solving all constraints as equalities 
B) always exists 
C) typically occurs in the interior of the feasible region 
D) occurs at a corner of the feasible region 
E) does not depend on all the constraints 
A) is determined by solving all constraints as equalities 
B) always exists 
C) typically occurs in the interior of the feasible region 
D) occurs at a corner of the feasible region 
E) does not depend on all the constraints D

Question 2

The manager of an appliance store wishes to obtain survey responses from a sample of at least 900 households regarding their future-purchase plans.The cost of mail surveys (M)is $1 each,while the cost of telephone surveys (T)is $3 per call.Response rates are 60% for telephone calls and 30% for mail questionnaires.To assure sufficient response accuracy,the manager insists on gathering at least three times as many actual telephone responses as mail responses.The manager's objective is to minimize the cost of the survey (C),while meeting the stipulated goals.Formulate and solve the firm's linear programming problem.

Accepted Answer

The response rates are 60% and 30% for telephone surveys and mail surveys respectively.So the respective response for each type of survey becomes 0.6T and 0.3M.Telephone responses (0.6T)should be at least three times as great as magazine responses (0.3M).It implies that 0.6T $\ge$ (3)(0.3M),or equivalently,T $\ge$ 1.5M.Therefore,the formulation is:
Minimize C = M + 3T
Subject to: 0.3M + 0.6T $\ge$ 900
T $\ge$ 1.5M; T,M $\ge$ 0
The two constraints establish the feasible region.Here,both constraints are binding because the slope of the objective function (-1/3)lies between the constraint slopes (-0.5 and 1.5 respectively).The optimal solution is: M = 750 mailings and T = 1,125 calls.The minimum total survey cost is $4,125.

Question 3

What must be done in order to identify the feasible region in a decision-variable plane?

Accepted Answer

A) Graph has to be plotted for all non-binding constraints. 
B) Objective function contours are to be plotted. 
C) Graph has to be plotted for all constraints with strict equality. 
D) Appropriate equations are to be solved simultaneously. 
E) One of the constraint functions is to made binding. 
A) Graph has to be plotted for all non-binding constraints. 
B) Objective function contours are to be plotted. 
C) Graph has to be plotted for all constraints with strict equality. 
D) Appropriate equations are to be solved simultaneously. 
E) One of the constraint functions is to made binding. C

Question 4

In a linear programming problem,maximize the objective function 2S + 3T,subject to the binding constraints S + T  700 and S + 2T  1,000.The optimal combination of decision variables for this optimization is _____.

Accepted Answer

A) S = 400 and T = 300 
B) S = 200 and T = 600 
C) S = 700 and T = 1000 
D) S = 0 and T = 1700 
E) S = 1700 and T = 0 
A) S = 400 and T = 300 
B) S = 200 and T = 600 
C) S = 700 and T = 1000 
D) S = 0 and T = 1700 
E) S = 1700 and T = 0

Question 5

In a linear programming problem,the objective function _____.

Accepted Answer

A) formulates the target in terms of the relevant decision variables 
B) restricts the values of decision variables 
C) shows the feasible region 
D) defines each resource constraint 
E) imposes the non-negativity condition on the decision variables 
A) formulates the target in terms of the relevant decision variables 
B) restricts the values of decision variables 
C) shows the feasible region 
D) defines each resource constraint 
E) imposes the non-negativity condition on the decision variables

Question 6

Determine the feasible region and the optimal corner of the following linear programming problem:
Minimize Z = 3x + 5y
Subject to: 2x + 5y $\ge$ 21
x + y $\ge$ 6
x $\ge$ 2 and y $\ge$ 0

Accepted Answer

The feasible region lies above the first

Question 7

A furniture manufacturer produces two types of tables.Table A sells for $430 and Table B for $300 per unit.Both types require 10 hours of labor.The hardwood requirement of Table A is $120 of per unit and that of Table B is $ per unit.The cost of labor is $10 an hour,and 400 labor hours are available per week.The firm's available supply of hardwood is $3,600 per week.Formulate,graph and solve the firm's linear programming problem.

Accepted Answer

The profit contribution for Table A is:

Question 8

Constrained optimization problems form the core of a distinct managerial field.This managerial field is known as _____.

Accepted Answer

A) decision theory 
B) research analysis 
C) operations research 
D) market analysis 
E) constraint analysis 
A) decision theory 
B) research analysis 
C) operations research 
D) market analysis 
E) constraint analysis

Question 9

Linear programming is useful for solving optimization problems involving _____.

Accepted Answer

A) both linear and nonlinear constraints 
B) linear constraints 
C) linear objective function but nonlinear constraints 
D) nonlinear objective function but linear constraints 
E) conventional calculus 
A) both linear and nonlinear constraints 
B) linear constraints 
C) linear objective function but nonlinear constraints 
D) nonlinear objective function but linear constraints 
E) conventional calculus

Question 10

A firm is mulling over its optimal mix of print advertising.Magazine ads (M)cost $2,500 each,reach an estimated 20,000 consumers,and generate about $7,500 revenue.Newspaper ads (N)cost $1,500 each,reach an estimated 15,000 consumers,and generate about $6,000 revenue.The advertising budget is $75,000 and management wishes to reach at least 600,000 consumers in total.In addition,the firm wants to have at least twice as many magazine ads as newspaper ads.Formulate the firm's linear programming problem.

Accepted Answer

The profit contributions are (7,500 - 2,

Question 11

In a linear programming problem,the goal to be maximized (or minimized)is referred to as the:

Accepted Answer

A) max-min function. 
B) constraint function. 
C) objective function. 
D) production function. 
E) algebraic function. 
A) max-min function. 
B) constraint function. 
C) objective function. 
D) production function. 
E) algebraic function.

Question 12

A discount appliance company is planning to advertise extensively before opening a new store.It has allocated $240,000 for advertising.The objective of the company is to maximize the total number of customers exposed to the firm's ads.Formulate a linear programming problem for the company given the matrix given below and find the optimal solution.
TYPE OF COST PER AD CUSTOMERS (1000s)MAXIMUM
ADVERTISING ($1000s)EXPOSED TO EACH AD NUMBER OF ADS
Radio (R)6 20 20
Television (T)16 40 15
Direct Mail (M)1 5 40
Newspaper (N 5 10 10________

Accepted Answer

Maximize Z = 20R + 40T + 5M + 10N
Subjec

Question 13

Which of the following concerning sensitivity analysis is incorrect?

Accepted Answer

A) It is used to study changes in the objective function with respect to per unit change in one or more coefficients. 
B) It is used to observe changes in the constraint function when the amount of an available resource is altered. 
C) It is used to calculate the shadow prices of the decision variables. 
D) It is used to derive the new optimal point of operation,when the objective function,or the constraint functions,or both change. 
E) It is used to identify the correct set of simultaneous equations. 
A) It is used to study changes in the objective function with respect to per unit change in one or more coefficients. 
B) It is used to observe changes in the constraint function when the amount of an available resource is altered. 
C) It is used to calculate the shadow prices of the decision variables. 
D) It is used to derive the new optimal point of operation,when the objective function,or the constraint functions,or both change. 
E) It is used to identify the correct set of simultaneous equations.

Question 14

What are shadow prices and why are they important? Explain.

Accepted Answer

A shadow price of a resource measures th

Question 15

Graph and solve the following linear programming problem:
Maximize Z = 100x + 50y
Subject to: 10x + 10y $\le$ 50
y $\le$ 3,x,y $\ge$ 0

Accepted Answer

The feasible region is a trapezoid in th

Question 16

A furniture manufacturer produces three types of chairs.Model A requires 1.2 hours of labor and 0.25 hour of machine time.Model B requires 1 hour of labor and 0.2 hour of machine time.Model C requires 0.8 hours of labor and 0.15 hours of machine time.There are 600 labor hours and 200 machine hours available per period.The manufacturer seeks to maximize profit and has determined that profit contributions of each unit of A,B,and C are $20,$15,and $12 respectively.Formulate as a linear program.

Accepted Answer

Maximize profit = 20A + 15B +

Question 17

Why are computer solutions necessary,now days,to solve linear programming problems?

Accepted Answer

The process of solving linear programmin

Question 18

The optimal combination of decision variables of a linear programming problem is x = 20 and y = 30.The given resource constraints are: 5x + 2y  150 and y  15.The shadow price of the second constraint is _____.

Accepted Answer

A) 1.5 
B) 0.67 
C) Zero 
D) 10 
E) 0.1 
A) 1.5 
B) 0.67 
C) Zero 
D) 10 
E) 0.1

Question 19

The linear programming method resembles the optimization problem.What are the common features that they incorporate?

Accepted Answer

A) Decision variables and objectives 
B) Conditional variables and objectives 
C) Constraints and decision variables 
D) Target variables and constraints 
E) Predictor variables and objectives 
A) Decision variables and objectives 
B) Conditional variables and objectives 
C) Constraints and decision variables 
D) Target variables and constraints 
E) Predictor variables and objectives

Question 20

If the shadow price of a given resource is $100 and the cost of expanding the capacity of that resource is $80 per unit,then the expansion of the capacity will _____.

Accepted Answer

A) earn positive profits 
B) earn zero profit,but the firm will stay in business. 
C) temporarily earn negative profits 
D) not be a rational decision 
E) not affect the profit level 
A) earn positive profits 
B) earn zero profit,but the firm will stay in business. 
C) temporarily earn negative profits 
D) not be a rational decision 
E) not affect the profit level

The optimal solution in a linear programming problem _____.

What must be done in order to identify the feasible region in a decision-variable plane?

In a linear programming problem,maximize the objective function 2S + 3T,subject to the binding constraints S + T  700 and S + 2T  1,000.The optimal combination of decision variables for this optimization is _____.

In a linear programming problem,the objective function _____.

Determine the feasible region and the optimal corner of the following linear programming problem: Minimize Z = 3x + 5y Subject to: 2x + 5y $\ge$ 21 x + y $\ge$ 6 x $\ge$ 2 and y $\ge$ 0

Constrained optimization problems form the core of a distinct managerial field.This managerial field is known as _____.

Linear programming is useful for solving optimization problems involving _____.

In a linear programming problem,the goal to be maximized (or minimized)is referred to as the:

Which of the following concerning sensitivity analysis is incorrect?

What are shadow prices and why are they important? Explain.

Graph and solve the following linear programming problem: Maximize Z = 100x + 50y Subject to: 10x + 10y $\le$ 50 y $\le$ 3,x,y $\ge$ 0

Why are computer solutions necessary,now days,to solve linear programming problems?

The optimal combination of decision variables of a linear programming problem is x = 20 and y = 30.The given resource constraints are: 5x + 2y  150 and y  15.The shadow price of the second constraint is _____.

The linear programming method resembles the optimization problem.What are the common features that they incorporate?

If the shadow price of a given resource is $100 and the cost of expanding the capacity of that resource is $80 per unit,then the expansion of the capacity will _____.

Introduction to Economic Decision Making

Optimal Decisions Using Marginal Analysis

Demand Analysis and Optimal Pricing

Estimating and Forecasting Demand

Production

Cost Analysis

Perfect Competition

Monopoly

Oligopoly

Game Theory and Competitive Strategy

Regulation, Public Goods, and Benefit-Cost Analysis

Decision Making Under Uncertainty

The Value of Information

Asymmetric Information and Organizational Design

Bargaining and Negotiation

Auctions and Competitive Bidding

Filters

Exam 17: Linear Programming

The optimal solution in a linear programming problem _____.

What must be done in order to identify the feasible region in a decision-variable plane?

In a linear programming problem,maximize the objective function 2S + 3T,subject to the binding constraints S + T  700 and S + 2T  1,000.The optimal combination of decision variables for this optimization is _____.

In a linear programming problem,the objective function _____.

Determine the feasible region and the optimal corner of the following linear programming problem: Minimize Z = 3x + 5y Subject to: 2x + 5y ≥\ge≥ 21 x + y ≥\ge≥ 6 x ≥\ge≥ 2 and y ≥\ge≥ 0

Constrained optimization problems form the core of a distinct managerial field.This managerial field is known as _____.

Linear programming is useful for solving optimization problems involving _____.

In a linear programming problem,the goal to be maximized (or minimized)is referred to as the:

Which of the following concerning sensitivity analysis is incorrect?

What are shadow prices and why are they important? Explain.

Graph and solve the following linear programming problem: Maximize Z = 100x + 50y Subject to: 10x + 10y ≤\le≤ 50 y ≤\le≤ 3,x,y ≥\ge≥ 0

Why are computer solutions necessary,now days,to solve linear programming problems?

The optimal combination of decision variables of a linear programming problem is x = 20 and y = 30.The given resource constraints are: 5x + 2y  150 and y  15.The shadow price of the second constraint is _____.

The linear programming method resembles the optimization problem.What are the common features that they incorporate?

If the shadow price of a given resource is $100 and the cost of expanding the capacity of that resource is $80 per unit,then the expansion of the capacity will _____.

Introduction to Economic Decision Making

Optimal Decisions Using Marginal Analysis

Demand Analysis and Optimal Pricing

Estimating and Forecasting Demand

Production

Cost Analysis

Perfect Competition

Monopoly

Oligopoly

Game Theory and Competitive Strategy

Regulation, Public Goods, and Benefit-Cost Analysis

Decision Making Under Uncertainty

The Value of Information

Asymmetric Information and Organizational Design

Bargaining and Negotiation

Auctions and Competitive Bidding

Filters

Determine the feasible region and the optimal corner of the following linear programming problem: Minimize Z = 3x + 5y Subject to: 2x + 5y $\ge$ 21 x + y $\ge$ 6 x $\ge$ 2 and y $\ge$ 0

Graph and solve the following linear programming problem: Maximize Z = 100x + 50y Subject to: 10x + 10y $\le$ 50 y $\le$ 3,x,y $\ge$ 0