Deck 13: Introduction to Prescriptive Analytics

Question 1

When using Excel to model uncertainty, the RAND function and BINOM.INV functions are used. What key is used to redraw new observations, changing the output?

A) Return key
B) ALT4
C) F4
D) F9

Answer 1

F9

Question 2

A CNBC study in 2017 determined only 35% of adults have zero to only a couple of hundred dollars in a savings account. With n = 4 and p = 0.43, using the binomial probability distribution, what is the mean and the standard deviation of the population? Hint: $\sigma$ = np(1 - p)

A) 4 and 0.98 respectively
B) 1.72 and 0.9902 respectively
C) 2 and 1.74 respectively
D) 1.8 and 0.9804 respectively

Answer 2

1.72 and 0.9902 respectively

Question 3

A CNBC study in 2017 determined only 35% of adults have zero to only a couple of hundred dollars in a savings account. With n = 5 and p = 0.35, using the binomial probability distribution, what is the mean and the standard deviation of the population? Hint: $\sigma$ =

A) 5 and 1.13 respectively
B) 1.75 and 1.0665 respectively
C) 2.50 and 1.1705 respectively
D) 1.55 and 1.1375 respectively

Answer 3

1.75 and 1.0665 respectively

Question 4

Lane Accessories has a growing demand for custom Apple watch designer bands. The current manufacturing costs are $140 per hour to operate, for each hour of operation, 205 black band designs and 180 multi-color designs are completed. However, Lane found a new larger manufacturing space that will cost $160 per hour and produce 325 black design bands and 289 multi-color bands per hour completed. Lane has newly placed orders to restock other retail outlets nationwide for 7,000 black band designs and 5,000 multi-color bands. Because Lane is out of inventory, she needs to decide how many hours to operate each facility to fulfill orders while minimizing cost. Formulate the minimization function for production costs.

A) Production Costs = 140x1 + 160x2
B) Production Costs = (140x1 + 385) + (160x2 + 614)
C) Production Costs = 385x1 + 614x2
D) Production Costs = (140x1 + 7,000) + (160x2 + 5,000)

Question 5

Lane Accessories has a growing demand for custom Apple watch designer bands. The current manufacturing costs are $120 per hour to operate, for each hour of operation, 210 black band designs and 180 multi-color designs are completed. However, Lane found a new larger manufacturing space that will cost $160 per hour and produce 325 black design bands and 289 multi-color bands per hour completed. Lane has newly placed orders to restock other retail outlets nationwide for 6,000 black band designs and 5,000 multi-color bands. Because Lane is out of inventory, she needs to decide how many hours to operate each facility to fulfill orders while minimizing cost. Formulate the minimization function for production costs.

A) Production Costs = 120x₁ + 160x₂
B) Production Costs = (120x₁ + 390) + (160x₂ + 614)
C) Production Costs = 390x₁ + 614x₂
D) Production Costs = (120x₁ + 6,000) + (160x₂ + 5,000)

Question 6

Which one of the following is not an essential component of linear programming?

A) random
B) an objective function
C) decision variables
D) constraints

Question 7

Lane Accessories has a growing demand for custom Apple watch designer bands. The current manufacturing costs are $130 per hour to operate, for each hour of operation, 245 black band designs and 180 multi-color designs are completed. However, Lane found a new larger manufacturing space that will cost $160 per hour and produce 325 black design bands and 289 multi-color bands per hour completed. Lane has newly placed orders to restock other retail outlets nationwide for 5,000 black band designs and 7,000 multi-color bands. Because Lane is out of inventory, she needs to decide how many hours to operate each facility to fulfill orders while minimizing cost. Formulate the orders for black design bands.

A) 245x1+325x2 $\ge$ 5,000x3
B) 245x1 + 325x2 $\ge$ 5,000
C) 180x1 + 245x2 $\ge$ 5,000
D) 180x1 + 325x2 $\ge$ 7,000

Question 8

Lane Accessories has a growing demand for custom Apple watch designer bands. The current manufacturing costs are $120 per hour to operate, for each hour of operation, 210 black band designs and 180 multi-color designs are completed. However, Lane found a new larger manufacturing space that will cost $160 per hour and produce 325 black design bands and 289 multi-color bands per hour completed. Lane has newly placed orders to restock other retail outlets nationwide for 6,000 black band designs and 5,000 multi-color bands. Because Lane is out of inventory, she needs to decide how many hours to operate each facility to fulfill orders while minimizing cost. Formulate the orders for black design bands.

A) 210x₁ + 325x₂ $\ge$ 6,000x₃
B) 210x₁ + 325x₂ $\ge$ 6,000
C) 180x₁ + 210x₂ $\ge$ 6,000
D) 180x₁ + 325x₂ $\ge$ 5,000

Question 9

Sampson Ltd produces two products that can be produced on either of two machines. Each month, only 500 hours of time are available on each machine. The time required to produce each item by hour and machine is:

The demand and price point for each product that customers are willing to pay are above. The company goal is to maximize revenue from sales from the next two months. Based on the provided information, how many constraints does this problem have excluding the non-negativity constraints?

A) 2 total constraints
B) 4 total constraints
C) 6 total constraints
D) 8 total constraints

Question 10

By viewing the following Excel snapshot, in Excel Solver what would be entered to formulate the Objective Function for E3?

A) =SUM(B5:D11,C8:D11)
B) =SUMPRODUCT(B5*C5) + (B8*C8)
C) =SUMPRODUCT(B5+B8) * (C5+C8)
D) =SUMPRODUCT(B5*B8) + (C5*C8)

Question 11

By viewing the following Excel snapshot, in Excel Solver what would be entered to formulate B11, Material (units) for Quantity?

A) =SUMPRODUCT(B2+B8) * (C2+C8)
B) =SUMPRODUCT(B2*B8) + (C2*C8)
C) =SUMPRODUCT(B2*D15) + (C2*D16)
D) =SUMPRODUCT(B2*D15) * (C2*D16)

Question 12

Based on the following sensitivity results on constraints, what is the optimal LP solution for Products 1 and 2?

A) Product 1: 290 units and Product 2: 234 units
B) Product 1: 425 units and Product 2: 140 units
C) Product 1: 290 units and Product 2: 140 units
D) Product 1: 125 units and Product 2: 84 units

Question 13

Based on the following sensitivity results on constraints, what is the optimal LP solution for Products 1 and 2?

A) Product 1: 300 units and Product 2: 234 units
B) Product 1: 425 units and Product 2: 150 units
C) Product 1: 300 units and Product 2: 150 units
D) Product 1: 125 units and Product 2: 84 units

Question 14

Based on the following sensitivity results on constraints, how would an increase in machine hours impact the LP solution?

A) The hours can have an infinite increase without altering the solution.
B) The hours can only decrease without altering the solution.
C) The hours can have an increase by 750 units before price decreases.
D) The hours cannot be predicted with the information presented.

Question 15

Based on the following Variable cells segment of a Solver Sensitivity Report, what range does Product 1 per-unit profit fall between at 400 units?

A) The range is between 0.881 and 0.74.
B) The range is between 0.881 and 6.74.
C) The range is between 5.119 and 6.74.
D) The range can only be determined with more details from the sensitivity report.

Question 16

Based on the following Variable cells segment of a Solver Sensitivity Report, what range does Product 1 per-unit profit fall between at 300 units?

A) The range is between 0.889 and 0.75.
B) The range is between 0.889 and 5.75.
C) The range is between 4.111 and 5.75.
D) The range can only be determined with more details from the sensitivity report.

Question 17

The Monte Carlo simulation is also known as

A) stochastic & probabilistic.
B) stochastic & deterministic.
C) deterministic.
D) probabilistic & deterministic.

Question 18

In a linear programming model, the parameter values in an objective function are referred to as the

A) objective function coefficients.
B) parameter function.
C) constraint coefficient.
D) quantitative function.

Question 19

At Taste of Thyme coffee shop a dirty chai latte creates a profit point of $2.83 for a small and $3.36 for a large. In a month, 225 small lattes were sold and 285 large lattes. As a fast growing demand item with fall approaching, the demand is estimated at 400 and 420 per month. The amount of machine time needed to produce the lattes is 5 minutes and 7 minutes each or for a month, 16.47 hours a month for a small and 33.25 hours a month for a large. What is the maximization function for profit?

A) Profit = 400x1 + 420x2
B) Profit = 2.83x1 + 3.36x2
C) Profit = 16.47x1 + 33.25x2
D) Profit = 2.48x1 + 3.06x2

Question 20

At Taste of Thyme coffee shop a dirty chai latte creates a profit point of $2.85 for a small and $3.80 for a large. In a month, 200 small lattes were sold and 285 large lattes. As a fast growing demand item with fall approaching, the demand is estimated at 400 and 420 per month. The amount of machine time needed to produce the lattes is 5 minutes and 7 minutes each or for a month, 16.67 hours a month for a small and 33.25 hours a month for a large. What is the maximization function for profit?

A) Profit = 400x₁ + 420x₂
B) Profit = 2.85x₁ + 3.80x₂
C) Profit = 16.67x₁ + 33.25x₂
D) Profit = 2.50x₁ + 3.50x₂

Question 21

At Taste of Thyme coffee shop a dirty chai latte creates a profit point of $2.79 for a small and $3.33 for a large. In a month, 240 small lattes were sold and 285 large lattes. As a fast growing demand item with fall approaching, the demand is estimated at 400 and 420 per month. The allotted machine time for both lattes is 110 hours. The amount of machine time needed to produce the lattes is 7 minutes and 7 minutes each or for a month, 16.67 hours a month for a small and 34.16 hours a month for a large. What is the corresponding parameters formulation for machine time?

A) 7x1 + 7x2 $\le$ 110
B) 16.67x1 + 34.16x2 $\ge$ 110
C) 2.79x1 + 3.38x2 $\le$ 110
D) 16.67x1 + 34.16x2 $\le$ 110

Question 22

At Taste of Thyme coffee shop a dirty chai latte creates a profit point of $2.85 for a small and $3.80 for a large. In a month, 200 small lattes were sold and 285 large lattes. As a fast growing demand item with fall approaching, the demand is estimated at 400 and 420 per month. The allotted machine time for both lattes is 90 hours. The amount of machine time needed to produce the lattes is 5 minutes and 7 minutes each or for a month, 16.67 hours a month for a small and 33.25 hours a month for a large. What is the corresponding parameters formulation for machine time?

A) 5x₁ + 7x₂ $\le$ 90
B) 16.67x₁ + 33.25x₂ $\ge$ 90
C) 2.85x₁ + 3.85x₂ $\le$ 90
D) 16.67x₁ + 33.25x₂ $\le$ 90

Question 23

Deterministic process is

A) created by random variable selection.
B) created by constraint identification.
C) a Monte Carlo simulation.
D) a precise estimation based on known variables.

Question 24

The first step in performing linear programming is

A) to generate random numbers.
B) to formulate a problem into a series of mathematical expressions.
C) to create intervals.
D) to analyze the file for patterns.

Question 25

Martin is evaluating 4 projects for potential capital funding. However, he only has $150,000 for Year one, and $55,000 for the remaining years to invest. Unfortunately, he cannot receive any additional funds unspent from year to year. Based on the following data, what is the constraint for the Year 1 integer programming formulation?

A) = $\Sigma$ i=14cixi
B) = $\Sigma$ i=14ai1xi ? 150,000
C) = $\Sigma$ i=14aixi ? 55,000
D) = $\Sigma$ i=14ai1xi ? 165,000

Question 26

Martin is evaluating 4 projects for potential capital funding. However, he only has $90,000 for Year one, and $50,000 for the remaining years to invest. Unfortunately, he cannot receive any additional funds unspent from year to year. Based on the following data, what is the constraint for the Year 1 integer programming formulation?

A) <p>=
B) <p>= $\le$ 90,000
C) <p>= $\le$ 50,000
D) <p>= $\le$ 165,000

Question 27

Martin is evaluating 4 projects for potential capital funding. However, he only has $100,000 for Year one, and $45,000 for the remaining three years to invest. Each of the four projects is projected to generate an expected return of $350,000, $400,000, $385,000, and $450,000 respectively. Based on the summary information provided, what is the Expected Return objective function?

A) Expected Return = $\Sigma$ i=14cixi
B) Expected Return = 100x1 + 45x2
C) Expected Return = $\Sigma$ i=x14cixi
D) Expected Return = $\Sigma$ i=1ai1xi6i

Question 28

Martin is evaluating 4 projects for potential capital funding. However, he only has $90,000 for Year one, and $50,000 for the remaining three years to invest. Each of the four projects is projected to generate an expected return of $350,000, $400,000, $385,000, and $450,000 respectively. Based on the summary information provided, what is the Expected Return objective function?

A) <p>Expected Return =
B) Expected Return = 90x₁ + 50x₂
C) <p>Expected Return =
D) <p>Expected Return =

Question 29

The following Excel Solver Results show capital projects selected for investment. When constructing the Solver parameters, the "subject to the constraints" need to be set. What two constraints are required?{MISSING IMAGE}

A) $G$8 AND B10:E10 = binary
B) B8:E8 = binary AND F2:F5 <= I2:I5
C) B10:E10 = binary AND F2:F5 => I2:I5
D) B10:E10 = binary AND F2:F5 <= I2:I5

Question 30

In Excel, the worksheet needs to be prepared prior to running the Solver. As such, the total (total return), cell G8, shows the total of the expected return for approved projects. What is the formula that must be set in G8 to capture the results accurately?

A) =SUM(B8:E8 * B10:E10)
B) =SUMPRODUCT(B8:E8, B10:E10)
C) =SUMPRODUCT(B8:E8 * B10:E10)
D) =SUMPRODUCT(B8:E8, G2:G5)

Question 31

Be it a capital project selection or a transportation, a manager's goals are what drives the projects. In IP the manager's goal translates to the ______ function in programming.

A) objective
B) fractional
C) matrix
D) transport

Question 32

Watkins Trucking has two warehouses that service four retail locations for Harmons Hardware. The first warehouse supplies up to 180 pallets a week and the second warehouse supplies 300 pallets a week. The orders received weekly from Harmons are 75 pallets for the 1^st location and 50 pallets for locations 2, 3, & 4. Formulate the objective function for the total shipping costs.

A) <p>Minimize: Total Shipping Cost =
B) <p>Minimize: Total Shipping Cost =
C) <p>Maximize: Total Shipping Cost =
D) <p>Maximize: Total Shipping Cost =

Question 33

When using R, how do you store shipping costs?

A) >unit.costs <- matrix(2.81, 3.32, 2.90, 2.88)
B) >unit.costs <- unit.costs(2.81, 3.32, 2.90, 2.88)
C) >unit.costs <- matrix(c(2.81, 3.32, 2.90, 2.88), nrow=2, byrow=TRUE)
D) >unit.costs <- unit.costs(2.81, 3.32, 2.90, 2.88), nrow=2, byrow=TRUE)

Question 34

When using R, how do you store shipping costs?

A) >unit.costs <- matrix(2.85, 3.32, 3.10, 2.90)
B) >unit.costs <- unit.costs(2.85, 3.32, 3.10, 2.90)
C) >unit.costs <- matrix(c(2.85, 3.32, 3.10, 2.90), nrow=2, byrow=TRUE)
D) >unit.costs <- unit.costs(2.85, 3.32, 3.10, 2.90), nrow=2, byrow=TRUE)

Question 35

In a LP solution, constraints with slack are called ________ constraints.

A) binding
B) nonbinding
C) surplus
D) overage

Question 36

If x₁ and x₂ are outside of the feasibility region, what does that mean?

A) The first constraint is a valid solution to be considered.
B) Solutions outside of the feasibility region can be considered as viable.
C) The farthest outside the feasibility region is the optimal solution.
D) Solutions outside of the feasibility region cannot be considered.

Question 37

As a manager, Mike uses linear programming (LP) to formulate a problem into a series of mathematical expressions. __________ refers to the choices or alternatives Mike selects to minimize or maximize the value of his goals.

A) Objective function
B) Decision variables
C) Optimization
D) Feasible region

Question 38

Numerical values that are associated with objective function, decision variables, and constraints are called _________.

A) parameters
B) binary
C) value
D) assumptions

Question 39

An integer programming model which involves selection of investment is classified as what type of problem?

A) clustering problem
B) transportation problem
C) integer problem
D) capital budgeting problem

Question 40

In a transportation model, when constructing the constraints, the points of demand are classified as _________.

A) transportation
B) destinations
C) origin
D) goal

Question 41

Prescriptive analytics is the process of using decision analysis tools to improve decision making.

Question 42

The Monte Carlo simulation relies solely on average values to capture risk and uncertainty.

Question 43

Binomial and Poisson distributions are the two most relevant probability distributions for Monte Carlo simulations.

Question 44

Continuous uniform distribution, also known as the rectangular distribution, captures the time that elapses between occurrences.

Question 45

Integer Programming, like Linear Programming, requires the analyst to round to the nearest integer for optimization.

Question 46

In Excel, random observations can be generated, however random seed cannot be set, requiring values to be cut and pasted.

Question 47

The objective function is a mathematical representation of an objective.

Question 48

Constraints with slack or surplus in the linear programming solutions are called binding constraints.

Question 49

The shadow price, or dual price, of a constraint is an indication of the change in the optimized value of an objective function in a one unit change in a binding constraint.