Mathematics Question

Post ID: 3205531

Overview

Decision variables

Question 1 options:

A)	tell how much or how many of something to produce, invest, purchase, hire, etc

B)	represent the values of the constraints

C)	measure the objective function

D)	must exist for each constraint

A section of output from The Management Scientist is shown here.

Variable	Lower Limit	Current Value	Upper Limit
1	60	100	120

What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

Question 2 options:

A)	Nothing. The values of the decision variables, the shadow prices, and the objective function will all remain the same

B)	The value of the objective function will change, but the values of the decision variables and the shadow prices will remain the same

C)	The same decision variables will be positive, but their values, the objective function value, and the dual prices will change

D)	The problem will need to be resolved to find the new optimal solution and dual price

A section of output from The Management Scientist is shown here.

Constraint	Lower Limit	Current Value	Upper Limit
2	240	300	420

What will happen if the right-hand-side for constraint 2 increases by 200?

Question 3 options:

A)	Nothing. The values of the decision variables, the shadow prices, and the objective function will all remain the same

B)	The value of the objective function will change, but the values of the decision variables and the shadow prices will remain the same

C)	The same decision variables will be positive, but their values, the objective function value, and the dual prices will change

D)	The problem will need to be resolved to find the new optimal solution and shadow price

In an all-integer linear program

Question 4 options:

A)	all objective function coefficients must be integer

B)	all right-hand side values must be integer

C)	all variables must be integer

D)	all objective function coefficients and right-hand side values must be integer

The ANOVA procedure is a statistical approach for determining whether or not

Question 5 options:

A)	the means of two samples are equal

B)	the means of two or more samples are equal

C)	the means of more than two samples are equal

D)	the means of two or more populations are equal

In hypothesis testing if the null hypothesis is rejected

Question 6 options:

A)	no conclusions can be drawn from the test

B)	the alternative hypothesis is true

C)	the data must have been accumulated incorrectly

D)	the sample size has been too small

In following estimated regression equation yˆ=b₀+b₁x

Question 7 options:

A)	b₁ is the slope

B)	b₁ is the intercept

C)	b₀ is the slope

D)	None of these alternatives is correct

Regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation

Yˆ= 30,000 + 4 X

The above equation implies that an

Question 8 options:

A)	increase of $4 in advertising is associated with an increase of $4,000 in sales

B)	increase of $1 in advertising is associated with an increase of $4 in sales

C)	increase of $1 in advertising is associated with an increase of $34,000 in sales

D)	increase of $1 in advertising is associated with an increase of $4,000 in sales

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

Question 9 options:

A)	one independent and one or more dependent variables are related

B)	several independent and several dependent variables are related

C)	one dependent and one or more independent variables are related

D)	None of these alternatives is correct

In regression analysis, the variable that is being predicted is the

Question 10 options:

	dependent variable
	independent variable
	intervening variable
	is usually x

In a regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is

Question 11 options:

0,4000

0,0256

2,56

A measure of goodness of fit for the estimated regression equation is the

Question 12 options:

A)	multiple coefficient of determination

B)	mean square due to error

C)	mean square due to regression

D)	sample size

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

Question 13 options:

t test

F test

C)	Either a t test or a chi-square test can be used

D)	chi-square test

A multiple regression model has the form yˆ=7+2x₁+9x₂

As x₁ increases by 1 unit (holding x₂ constant), y is expected to

Question 14 options:

A)	increase by 9 units

B)	decrease by 9 units

C)	increase by 2 units

D)	decrease by 2 units

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each.

Formulate the mathematical model that maximizes the total profit. The numbers of bears claws and almond –filled croissants are whole numbers

Question 15 options:

A)	MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400

B)	MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400 B≥0,C≥0,B,C are integer numbers

C)	MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400 B≥0,C≥0

D)	MAX Z = $.20B + $.30C s.t. 6B + 3C ≥6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400 B≥0,C≥0,B,C are integer numbers

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S):

MAX 50R + 75S

s.t.

1.2 R + 1.6 S ≤ 600 assembly (hours)

0.8 R + 0.5 S ≤ 300 paint (hours)

.16 R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:


		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coefficient	Increase	Decrease
$B$7	Regular =	291.67	0.00	50	70	20
$C$7	Super =	133.33	0.00	75	50	43.75


		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$E$3	Assembly (hr/unit)	563.33	0.00	600	1E+30	36.67
$E$4	Paint (hr/unit)	300.00	33.33	300	39.29	175
$E$5	Inspect (hr/unit)	100.00	145.83	100	12.94	40

The optimal number of regular products to produce, the optimal number of super products to produce and total profits are respectively

Question 16 options:

A)	R=50, S=70, P=20

B)	R=50, S=75, P=43.75

C)	R=75, S=50, P=43.75

D)	R=291.67, S=133.33, P= $24,583

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S):

MAX 50R + 75S

s.t.

1.2 R + 1.6 S ≤ 600 assembly (hours)

0.8 R + 0.5 S ≤ 300 paint (hours)

.16 R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:


		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coefficient	Increase	Decrease
$B$7	Regular =	291.67	0.00	50	70	20
$C$7	Super =	133.33	0.00	75	50	43.75

		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$E$3	Assembly (hr/unit)	563.33	0.00	600	1E+30	36.67
$E$4	Paint (hr/unit)	300.00	33.33	300	39.29	175
$E$5	Inspect (hr/unit)	100.00	145.83	100	12.94	40

17. Select correct number.

The profit on the super product could increase by ________ without affecting the product mix.

Question 17 options:

$20

$50

$70

$43.75

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S):

MAX 50R + 75S

s.t.

1.2 R + 1.6 S ≤ 600 assembly (hours)

0.8 R + 0.5 S ≤ 300 paint (hours)

.16 R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:


		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coefficient	Increase	Decrease
$B$7	Regular =	291.67	0.00	50	70	20
$C$7	Super =	133.33	0.00	75	50	43.75

		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$E$3	Assembly (hr/unit)	563.33	0.00	600	1E+30	36.67
$E$4	Paint (hr/unit)	300.00	33.33	300	39.29	175
$E$5	Inspect (hr/unit)	100.00	145.83	100	12.94	40

Select correct number.

If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by ________.

Question 18 options:

$1,333

$58,332

$300

Consider the following linear program, which maximizes profit for two products--regular (R) and super (S):

MAX 50R + 75S

s.t.

1.2 R + 1.6 S ≤ 600 assembly (hours)

0.8 R + 0.5 S ≤ 300 paint (hours)

.16 R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:


		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coefficient	Increase	Decrease
$B$7	Regular =	291.67	0.00	50	70	20
$C$7	Super =	133.33	0.00	75	50	43.75

		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$E$3	Assembly (hr/unit)	563.33	0.00	600	1E+30	36.67
$E$4	Paint (hr/unit)	300.00	33.33	300	39.29	175
$E$5	Inspect (hr/unit)	100.00	145.83	100	12.94	40

19. Select correct number.

A change in the market has increased the profit on the super product by $5. Total profit will increase by ________.

Question 19 options:

$ 25249.9

$300

$667

$100

[Image unavailable: LP GRAPH]Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

	Machine Shop	Fabrication	Assembly
Tractor	2 hours	2 hours	1 hour
Lawn Mower	1 hour	3 hours	0 hour
Hrs.Available	60 hours	120 hours	45 hours

Formulation:

Let x = number of tractors produced per period

y = number of lawn mowers produced per period

MAX 30x + 30y

subject to 2x + y ≤ 60

2x + 3y ≤ 120

x ≤ 45

The graphical solution is shown below.

Using the graphical solution how many tractors and lawn mowers should be produced to maximize profit, and how much profit will they make?

Question 20 options:

A)	15 tractors and 30 lawn mowers for $1350 in profit

B)	30 tractors and 15 lawn mowers for $1050 in profit

C)	15 tractors and 30 lawn mowers for $1050 in profit

D)	30 tractors and 15 lawn mowers for $1350 in profit

ANOVA
	*Source of Variation*	SS	df	MS	*p-value*	F	*F critical*
	Between Groups	49.659	3		0.1897		2.84
	Within Groups	397.5
	Total	447.159	43

Using ANOVA table above please compute

MSTR

Question 21 options:

	16.553
	9.937
	11.3456
	12.091

ANOVA
	*Source of Variation*	SS	df	MS	*p-value*	F	*F critical*
	Between Groups	49.659	3		0.1897		2.84
	Within Groups	397.5
	Total	447.159	43

Using ANOVA table above please compute

22. F test

Question 22 options:

16.553

1.6657

12.091

11.3456

ANOVA
	*Source of Variation*	SS	df	MS	*p-value*	F	*F critical*
	Between Groups	49.659	3		0.1897		2.84
	Within Groups	397.5
	Total	447.159	43

Using ANOVA table above please compute

23. At 95% confidence test to determine whether there is a significant difference in the means of the three populations using ANOVA table using p-value approach.

Question 23 options:

A)	Since the p-value 0.1897 < 0.05, do not reject H_o, there is not a significant difference at 95% confidence

B)	Since the p-value 0.1897 > 0.05, do not reject H_o, there is not a significant difference in the means of the three populations at 95% confidence

C)	Since the p-value 0.1897 > 0.05, do not reject H_o

D)	Non of these alternatives is correct

A microcomputer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three independent variables. The three independent variables are price per unit (Price in $100s), advertising (ADV in $1,000s) and the number of product lines (Lines). Part of the regression results is shown below.

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

24. Use the above results and select the regression equation that can be used to predict sales

Question 24 options:

A)	Y=1.0211-0.1524Price+0.8849ADV-0.1463Lines

B)	Y=1.0211+0.1542Price-0.8849ADV

C)	Y=1.0211+0.1542Price-0.8849ADV-0.1463Line

D)	Non of these alternatives is correct

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

25. What has been the sample size for this analysis?

Question 25 options:

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

26. Compute the coefficient of determination and fully interpret its meaning

Question 26 options:

A)	0.188; 18.8% of the variation in sales is explained by variations in the three independent variables

B)	0.312; 31.2% of the variation in sales is explained by variations in the three independent variables

C)	0.488; 48.8% of the variation in sales is explained by variations in the three independent variables

D)	Non of these alternatives is correct

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

27. At α = 0.05,conduct t- test to see if there is a significant relationship between sales and the number of product lines. ; p-value is between .2 and .4. What is your conclusion?

Question 27 options:

A)	t = -0.027; p-value is between .2 and .4; do not reject H₀; not significant at α = 0.05

B)	t = 0.031; p-value is between .2 and .4; do not reject H₀; not significant at α = 0.05

C)	t = -0.095; p-value is between .2 and .4; do not reject H₀; not significant at α = 0.05

D)	Non of these alternatives is correct

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

28. At α = 0.05, conduct t-test to see if there is a significant relationship between sales and unit price. If p-value between .2 and .4 what is your conclusion?

Question 28 options:

A)	t = -1.08; p-value is between .2 and .4; do not reject H₀; not significant at α = 0.05

B)	t = -3.28; p-value is between .2 and .4; do not reject H₀; not significant at α = 0.05

C)	t = 2.68; p-value is between .2 and .4; reject H₀; it’s significant at α = 0.05

D)	t = -1.56; p-value is between .2 and .4; reject H₀; it’s significant at α = 0.05

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

29. Is the regression model significant? (Perform an F test.) What is your conclusion if p-value is between .01 and .025?

Question 29 options:

A)	F = 3.45; p-value is between .01 and .025; reject H₀; model is not significant at α = 0.05

B)	F = 2.15; p-value is between .01 and .025; reject H₀; model is significant

C)	F = 4.45; p-value is between .01 and .025; reject H₀; model is significant at α = 0.05

D)	Non of these alternatives is correct

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price	-0.1524	0.1411
ADV	0.8849	0.2886
Lines	-0.1463	1.5340
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares
Regression		2708.61
Error (Residuals)	14	2840.51

30. Fully interpret (coefficient of price) per unit that is, the slope for the price per unit

Question 30 options:

A)	As the price is increased by $100, sales are expected to increase by $1,524.50

B)	As the price is increased by $1, sales are expected to decrease by $1,524.50

C)	As the price is increased by $200, sales are expected to increase by $1,524.50

D)	As the price is increased by $100, sales are expected to decrease by $1,524.50

The following data summarizes the historical demand for a product:

Month	Actual Demand
March	20
April	25
May	40
June	35
July	30
August	45

31. Use a four-period moving average to determine the forecasted demand for July, August, and September. Select correct answer and show all your calculations with details.

Question 31 options:

A)	July forecast = 32.5; August forecast = 33.5; September forecast = 37.5

B)	July forecast = 31.33; August forecast = 34.5; September forecast = 37.5

C)	July forecast = 30; August forecast = 33.5; September forecast = 40.5

D)	July forecast = 30; August forecast = 32.5; September forecast = 37.5

The following data summarizes the historical demand for a product:

Month	Actual Demand
March	20
April	25
May	40
June	35
July	30
August	45

32. If the forecasted demand for June, July, and August is 32, 38 and 42, respectively, what is MSE? Select correct answer and show all your calculations with details.

Question 32 options:

A)	MSE = 15.13

B)	MSE = 17.32

C)	MSE = 27.33

D)	Non of these alternatives is correct

A payoff table of maximization problem is given as

	State of Nature
Decision	s₁	s₂	s₃
d₁	10	8	6
d₂	14	15	2
d₃	7	8	9

Notes: this isa maximization problem. Show all your calculations with details and select correct answers.

33. What decision should be made by the optimistic decision maker?

Question 33 options:

select d₂

select d₁

select d₃

D)	Non of these alternatives is correct

A payoff table of maximization problem is given as

	State of Nature
Decision	s₁	s₂	s₃
d₁	10	8	6
d₂	14	15	2
d₃	7	8	9

Notes: this isa maximization problem. Show all your calculations with details and select correct answers.

34. What decision should be made by the conservative decision maker?

Question 34 options:

select d₁

select d₂

select d₃

D)	Non of these alternatives is correct

A payoff table of maximization problem is given as

	State of Nature
Decision	s₁	s₂	s₃
d₁	10	8	6
d₂	14	15	2
d₃	7	8	9

Notes: this isa maximization problem. Show all your calculations with details and select correct answers.

35. What decision should be made under minimax regret?

Question 35 options:

A)	d₁ or d₂ or d₃

d₂

d₁

D)	Non of these alternatives is correct

A payoff table of maximization problem is given as

	State of Nature
Decision	s₁	s₂	s₃
d₁	10	8	6
d₂