Indicate whether the statement is true or false.<\/p>\n
1.\u00a0 An extreme point of the feasible region can include negative values of coordinates.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
2.\u00a0In stationary time series there is no significant upward or downward trend in the data over time.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
3.\u00a0Mathematical programming is an approach\u00a0that involves determining how to allocate the resources in such a way as to maximize profits or minimize costs.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
4.\u00a0Examining the effect of changes in the RHS values of constraints is part of the answer report.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
5.\u00a0The TREND( ) function can be used to calculate the estimated values for linear regression models.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
6.\u00a0Shadow prices represent the marginal values of the resources in an LP problem,
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
7.\u00a0Seasonality is a regular, repeating pattern in the data that takes longer than 1 year to complete.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
8.\u00a0Objective cell, variable cells and constraint cells are terms used in Excel solver to describe the purpose of the cells.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
9.\u00a0Solver can be used to estimate model parameters when the time series is stationary and additive seasonal effects are present.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
10.\u00a0The weighted moving average technique is a special case of the moving average technique.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
11.\u00a0If a shadow price is positive for a maximization problem, a unit increase in the RHS value of the associated constraint results in a decrease in the optimal objective function value.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
12.\u00a0 Good decisions always result in good outcomes.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
13.\u00a0 Humans\u00a0usually do not make errors in estimation due to anchoring and framing effects.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
14.\u00a0 Excel and other spreadsheets contain an add-on called solver.
\na.\u00a0 True
\nb.\u00a0 False<\/p>\n
Indicate the answer choice that best completes the statement or answers the question.<\/p>\n
Exhibit 3.1<\/p>\n
The following questions are based on this problem and accompanying Excel windows.<\/p>\n
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.<\/p>\n
Let X1 = Number of Beds to produce
\nX2 = Number of Desks to produce<\/p>\n
The LP model for the problem is<\/p>\n
MAX: 30 X1 + 40 X2
\nSubject to: 6 X1 + 4 X2 \u2264 36 (carpentry)
\n4 X1 + 8 X2 \u2264 40 (varnishing)
\nX2 \u2264 8 (demand for desks)
\nX1, X2 \u2265 0<\/p>\n
A B C D E
\n1 \u00a0 Jones Furniture
\n2
\n3 \u00a0 Beds Desks
\n4 Number to make: \u00a0 \u00a0 \u00a0 Total Profit:
\n5 Unit profit: 30 40
\n6
\n7 Constraints: \u00a0 \u00a0 Used Available
\n8 Carpentry 6 4 \u00a0 36
\n9 Varnishing 4 8 \u00a0 40
\n10 Desk demand \u00a0 1 \u00a0 8
\n15.\u00a0Refer to Exhibit 3.1. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?
\na.\u00a0 =B4*B5+C4*C5
\nb.\u00a0 =SUMPRODUCT(B8:C8,$B$4:$C$4)
\nc.\u00a0 =SUM(B5:C5)
\nd.\u00a0 =SUM(E8:E10)<\/p>\n
16.\u00a0Why would someone wish to use a spreadsheet model?
\na.\u00a0 To implement a computer model.
\nb.\u00a0 Because spreadsheets are convenient.
\nc.\u00a0 To analyze decision alternatives.
\nd.\u00a0 All of these.<\/p>\n
17.\u00a0In a model Y=f(x1, x2), Y is called:
\na.\u00a0 a dependent variable.
\nb.\u00a0 an independent variable.
\nc.\u00a0 a confounded variable.
\nd.\u00a0 a convoluted variable.<\/p>\n
18.\u00a0In a mathematical formulation of an optimization problem, the objective function is written as z=2×1+3×2. Then:
\na.\u00a0 x1 is a decision variable
\nb.\u00a0 x2 is a parameter
\nc.\u00a0 z needs to be maximized
\nd.\u00a0 2 is a first decision variable level<\/p>\n
20.\u00a0What needs to be done to the two constraints in order to convert the problem to a standard form?<\/p>\n
MAX: 8 X1 + 4 X2
\nSubject to: 5 X1 + 5 X2 \u2264 20
\n6 X1 + 2 X2 \u2264 18
\nX1, X2 \u2265 0
\na.\u00a0 a slack variable needs to be added to each constraint to convert them to equalities.
\nb.\u00a0 nothing.
\nc.\u00a0 they need to be combined to a single constraint.
\nd.\u00a0 they need to be subtracted side-by-side<\/p>\n
Exhibit 3.3<\/p>\n
The following questions are based on this problem and accompanying Excel windows.<\/p>\n
Jack’s distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer’s requirements and maximize profit.<\/p>\n
Let X1 = Number of liters of product A in total blend delivered
\nX2 = Number of liters of product B in total blend delivered<\/p>\n
MIN: 7 X1 + 3 X2
\nSubject to: X1 + X2 = 1.5 * 50 (Total liters of mix)
\nX1 \u2265 0.48 * 1.5 * 50 (X1 minimum)
\nX2 \u2265 0.5 * 50 (X2 minimum)
\n.0.95 X1 + 0.78 X2 \u2265 0.85 * 1.5 * 50 (85% alcohol minimum)
\nX1, X2 \u2265 0<\/p>\n
A B C D E
\n1 \u00a0 Jacks’ Distillery
\n2
\n3 \u00a0 A B
\n4 Liters to use \u00a0 \u00a0 \u00a0 Total Cost:
\n5 Unit cost: 10.5 4.5
\n6
\n7 Constraints: \u00a0 \u00a0 Supplied Requirement
\n8 Total Liters 1 1 \u00a0 75
\n9 A required 1 \u00a0 \u00a0 36
\n10 B required \u00a0 1 \u00a0 25
\n11 85% alcohol 0.95 0.78 \u00a0 63.75
\n2
\n3 \u00a0 A B
\n4 Liters to use \u00a0 \u00a0 \u00a0 Total Cost:
\n5 Unit cost: 10.5 4.5
\n6
\n7 Constraints: \u00a0 \u00a0 Supplied Requirement
\n8 Total Liters 1 1 \u00a0 75
\n9 A required 1 \u00a0 \u00a0 36
\n10 B required \u00a0 1 \u00a0 25
\n11 85% alcohol 0.95 0.78 \u00a0 63.75
\n21.\u00a0Refer to Exhibit 3.3. What formula should be entered in cell D11 in the accompanying Excel spreadsheet to compute the total liters of alcohol supplied?
\na.\u00a0 =B4*B5+C4*C5
\nb.\u00a0 =SUMPRODUCT(B11:C11,$B$4:$C$4)
\nc.\u00a0 =SUM(B5:C5)
\nd.\u00a0 =SUM(E8:E10)<\/p>\n
22.\u00a0Binding constraints have
\na.\u00a0 zero slack.
\nb.\u00a0 negative slack.
\nc.\u00a0 positive slack.
\nd.\u00a0 surplus resources.<\/p>\n
24.\u00a0A linear formulation means that:
\na.\u00a0 the objective function and all constraints must be linear
\nb.\u00a0 only the objective function must be linear
\nc.\u00a0 at least one constraint must be linear
\nd.\u00a0 no more than 50% of the constraints must be linear<\/p>\n
26.\u00a0Which step of the problem-solving process is considered the most important?
\na.\u00a0 Identify problem.
\nb.\u00a0 Analyze model.
\nc.\u00a0 Test results.
\nd.\u00a0 Implement solution.<\/p>\n
28.\u00a0The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.<\/p>\n
X1 = number of product 1 produced in each batch
\nX2 = number of product 2 produced in each batch<\/p>\n
MAX: 150 X1 + 250 X2
\nSubject to: 2 X1 + 5 X2 \u2264 200
\n3 X1 + 7 X2 \u2264 175
\nX1, X2 \u2265 0
\nHow much profit is earned per each unit of product 2 produced?
\na.\u00a0 150
\nb.\u00a0 175
\nc.\u00a0 200
\nd.\u00a0 250<\/p>\n
29.\u00a0The symbols X1, Z1, Dog are all examples of
\na.\u00a0 decision variables.
\nb.\u00a0 constraints.
\nc.\u00a0 objectives.
\nd.\u00a0 parameters.<\/p>\n
30.\u00a0Which of the following categories of modeling techniques involves determining the value of a dependent variable based on specific values of independent variables?
\na.\u00a0 Biased models.
\nb.\u00a0 Descriptive models.
\nc.\u00a0 Predictive models.
\nd.\u00a0 Prescriptive models.<\/p>\n
31.\u00a0When performing sensitivity analysis, which of the following assumptions must apply?
\na.\u00a0 All other coefficients remain constant.
\nb.\u00a0 Only right hand side changes really mean anything.
\nc.\u00a0 The X1 variable change is the most important.
\nd.\u00a0 The non-negativity assumption can be relaxed<\/p>\n
32.\u00a0The first step in formulating a linear programming problem is
\na.\u00a0 Identify any upper or lower bounds on the decision variables.
\nb.\u00a0 State the constraints as linear combinations of the decision variables.
\nc.\u00a0 Understand the problem.
\nd.\u00a0 Identify the decision variables.
\ne.\u00a0 State the objective function as a linear combination of the decision variables.<\/p>\n
33.\u00a0Mathematical programming is referred to as
\na.\u00a0 optimization.
\nb.\u00a0 satisficing.
\nc.\u00a0 approximation.
\nd.\u00a0 simulation.<\/p>\n
Exhibit 3.2<\/p>\n
The following questions are based on this problem and accompanying Excel windows.<\/p>\n
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 only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.<\/p>\n
Maximum \u00a0 Assembly Inspection
\nComputer Profit per demand for Wiring Hours Hours Hours
\nModel Model ($) product Required Required Required
\nPlain 30 80 .4 .5 .2
\nFancy 40 90 .5 .4 .3
\nHours Available 50 50 22<\/p>\n
Let X1 = Number of Plain computers to produce
\nX2 = Number of Fancy computers to produce<\/p>\n
MAX: 30 X1 + 40 X2
\nSubject to: .4 X1 + .5 X2 \u2264 50 (wiring hours)
\n.5 X1 + .4 X2 \u2264 50 (assembly hours)
\n.2 X1 + .2 X2 \u2264 22 (inspection hours)
\nX1 \u2264 80 (Plain computers demand)
\nX2 \u2264 90 (Fancy computers demand)
\nX1, X2 \u2265 0<\/p>\n
A B C D E
\n1 \u00a0 Byte Computer Company
\n2
\n3 \u00a0 Plain Fancy
\n4 Number to make: \u00a0 \u00a0 \u00a0 Total Profit:
\n5 Unit profit: 30 40
\n6
\n7 Constraints: \u00a0 \u00a0 Used Available
\n8 Wiring 0.4 0.5 \u00a0 50
\n9 Assembly 0.5 0.4 \u00a0 50
\n10 Inspection 0.2 0.3 \u00a0 22
\n11 Plain Demand 1 \u00a0 \u00a0 80
\n12 Fancy Demand \u00a0 1 \u00a0 90
\n34.\u00a0Refer to Exhibit 3.2. Which of the following statements will represent the constraint for just assembly hours?
\na.\u00a0 B4:C4 \u2264 B5:C5
\nb.\u00a0 D9 \u2264 E9
\nc.\u00a0 D8:D10 \u2264 E8:E10
\nd.\u00a0 E8:E10 \u2264 D8:D10<\/p>\n
36.\u00a0A solvable problem must have:
\n\u200b
\na.\u00a0 a feasible region that is not an empty set.
\nb.\u00a0 the best solution.
\nc.\u00a0 no more than two constraints.
\nd.\u00a0 no more than two decision variables.<\/p>\n
37.\u00a0The coefficients in an LP model (cj, aij, bj) represent
\na.\u00a0 random variables.
\nb.\u00a0 numeric constants.
\nc.\u00a0 random constants.
\nd.\u00a0 numeric variables.<\/p>\n
38.\u00a0If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?
\na.\u00a0 increase of 100
\nb.\u00a0 increase of 110
\nc.\u00a0 decrease of 100
\nd.\u00a0 increases but by unknown amount<\/p>\n
42.\u00a0A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.<\/p>\n
Investment Return Years to Maturity Rating
\nA 6.45% 6 1-Excellent
\nB 8.50% 5 3-Good
\nC 9.00% 8 4-Fair
\nD 7.75% 4 2-Very Good
\n\u200b
\nFormulate the LP for this problem.<\/p>\n
44.\u00a0A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.<\/p>\n
Time period Required # of Nurses Wage ($\/hr)
\n12 am \u2212 4 am 20 15
\n4 am \u2212 8 am 30 16
\n8 am \u2212 12 pm 40 13
\n12 pm \u2212 4 pm 50 13
\n4 pm \u2212 8 pm 40 14
\n8 pm \u2212 12 am 30 15
\nWhat values would you enter in the Analytic Solver Platform (ASP) task pane for the following cells for this Excel spreadsheet implementation of the formulation for this problem?<\/p>\n
Objective Cell:<\/p>\n
Variables Cells:<\/p>\n
Constraints Cells:<\/p>\n
Let Xi = number of nurses working in time period i; i = 1,6<\/p>\n
MIN: 1X1 + 1X2 + 1X3 + 1X4 + 1X5 + 1X6
\nSubject to: 1X1 + 1X2 \u2265 30
\n1X2 + 1X3 \u2265 40
\n1X3 + 1X4 \u2265 50
\n1X4 + 1X5 \u2265 40
\n1X5 + 1X6 \u2265 30
\n1X1 + 1X6 \u2265 20
\nXi \u2265 0
\n\u200b
\nA B C D E F G H I
\n1 \u00a0 \u00a0 \u00a0 Nurse Hiring
\n2
\n3 \u00a0 Hours for each shift
\n4 \u00a0 Mid 4am 8am Noon 4pm 8pm Nurses Wages per
\n5 Shift 4am 8am Noon 4pm 8pm Mid Scheduled Nurse
\n6 1 1 1 0 0 0 0 \u00a0 $15
\n7 2 0 1 1 0 0 0 \u00a0 $16
\n8 3 0 0 1 1 0 0 \u00a0 $13
\n9 4 0 0 0 1 1 0 \u00a0 $13
\n10 5 0 0 0 0 1 1 \u00a0 $14
\n11 6 1 0 0 0 0 1 \u00a0 $15
\n12 Available: \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0Total Wages:
\n13 Required: 20 30 40 50 40 30<\/p>\n
46.\u00a0Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert’s grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert’s task somewhat by adding the following stipulations:<\/p>\n
\u2219 homework can account for up to 25% of the grade, but must be at least 5% of the grade;
\n\u2219 the project can account for up to 25% of the grade, but must be at least 5% of the grade;
\n\u2219 the mid-term and final must each account for between 10% and 40% of the grade but cannot account for more than 70% of the grade when the percentages are combined; and
\n\u2219 the project and final exam grades may not collectively constitute more than 50% of the grade.
\nFormulate an LP model for Robert to maximize his numerical grade.<\/p>\n","protected":false},"excerpt":{"rendered":"
QUANTITATIVE ANALYSIS For BUSINESS OPERATIONS Indicate whether the statement is true or false. 1.\u00a0 An extreme point of the feasible region can include negative values of coordinates. a.\u00a0 True b.\u00a0 False 2.\u00a0In stationary time series there is no significant upward Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"class_list":["post-433086","post","type-post","status-publish","format-standard","hentry","category-essay-paper-writing"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/433086","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=433086"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/433086\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=433086"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=433086"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=433086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}