QMB Modules 9-14 Final Exam
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. 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.
210x1 + 325x2 ≥ 6,000
Events are considered __________blank if they include all outcomes in the sample space.
exhaustive
Milton's Automotive Parts buys break lights for Ford Trucks from the manufacturer at $15 each and the company has $30 in daily labor associated with sales of the break lights. The brake lights sell for $30 each. What is the break even point?
2
The process of applying a set of analytical techniques for the development of machine learning and artificial intelligence is called data mining.
True
The process of computing the derivative is called differentiation
True
Modeling Stage 2: Analysis of the Model
We use mathematical methods to solve mathematical model. A variety tools are used
The calculated average error measuring the average magnitude of errors in predictive performance measures is called
mean absolute deviation
In a linear programming model, the parameter values in an objective function are referred to as the
objective function coefficients. - The objective coefficient is the alternate name for the parameter value in the objective function.
Numerical values that are associated with objective function, decision variables, and constraints are called _____________
parameters - Parameters or input parameters, are numerical values associated with all three. For example, 30 minutes to make a breakfast is a parameter value for the labor constraint
Tess is tasked with analyzing a data set with multiple variables with various scales. To reduce the difference in scale in variables, she is following a common process called _____________to make the observations unit-free.
standardizing - Standardizing or normalizing the numerical set before calculating is a common process to make the observations unit-free.
At Tasty Sweets ice cream shop, a banana split creates a profit point of $1.75 for a small and $2.50 for a large. Last month, 100 small banana splits and 185 large banana splits were sold. However, with summer approaching, the demand is estimated to increase. The maximum allotted labor for both banana splits sizes is 50 hours for the month. Based on last month's sales the amount of labor needed to produce one small and large banana split is 3 minutes and 5 minutes, respectively for a total of 5 hours a month for a small and 15.416 hours a month for a large. What is the corresponding constraint for monthly labor?
5x1 + 15.416x2 ≤ 50 - The preparation constraint is 5x1 + 15.416x2 ≤ 50, which takes the total monthly labor hours for a small banana split times the decision variable (number of small banana splits x1) plus the large banana split monthly labor hours times the decision variable (number of large banana splits x2).
If ŷ = 110 − 5x with y = product and x = price of product, what happens to the demand if the price is increased by 3 units?
Ans: Decreases by 15 units - Three times five is 15 units and the demand decreases due to the negative sign before the 5x.
Modeling Stage 3: Interpretation
Any conclusions that may be drawn for the analysis are applied to the original real-world problem, both to gauge the accuracy of the model and to make predictions
Based on the following table, what is the sample regression equation?
Earnings = 10,004.9665 + 0.4349Cost + 178.0989Grad + 141.4783Debt - the numbers in the coefficients column are applied to the formula
Molly e-mailed her clients offering a free 30-minute massage for referrals. In the following validation set of 100, Class 1 reflects the clients predicted to provide referrals and Class 0 reflects the clients predicted to not provide referrals. Based on the confusion matrix, what was the False Negative (FN) of current clients who provided referrals for a free message?
FN = 11: There are 11 current clients who provided referrals for free messages that were misclassified as clients who would not provide referrals.
The revenue is obtained from selling x units at unit price p(x) is the total cost divided by the number of units produced.
False
Constraints with slack or surplus in the linear programming solutions are called binding constraints.
False - Constraints with slack or surplus are called nonbinding constraints. Therefore, no optimal solution is on the line for the constraint.
For a function f(x) that is not linear, the rate of change is constant and conforms with x.
False - For a function f(x) that is linear, the rate of change is constant and conforms with x.
If the function f is differentiable at x=c, then f is increasing at x = c if f'(c) <0
False - If the function f is differentiable at x=c, then f is increasing at x = c if f'(c) >0 If the function f is differentiable at x=c, then f is decreasing at x = c if f'(c) <0
A __________________consists of a set of inputs and outputs and a rule. The rule must connect inputs and outputs such that for each input, there is exactly one corresponding output.
Function
Modeling Stage 1: Formulation
Given a real-world situation, we make enough simplifying assumptions to allow a mathematical formulation.
Smith Industries has a growing demand for custom athleisure wear. The current manufacturing costs are $90 per hour to operate, for each hour of operation, 110 black yoga pants and 150 multi-color yoga pants per hour are completed. However, Smith found a new larger space that will cost $125 per hour and produce 175 black yoga pants and 140 multi-color yoga pants per hour. Smith has newly placed orders to restock retail outlets for 4,000 black pants and 3,500 multi-color pants. Because Smith 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.
Production Costs = 90x1 + 125x2, is the minimization function
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?
Profit = 2.85x1 + 3.80x2 - Profit = 2.85x1 + 3.80x2, which reflects the price for the two products where x1 and x2 represents the decision variables for the number that will be produced.
Which one of the following is NOT an essential component of linear programming?
Random Are: The missing linear programming essential component is parameters. Parameters are numerical values associated with the objective, decision, and constraints.
What is the probability when a personal assessment is made without referencing data?
Subjective probability - Subjective probability is assigning a probability without referencing any data.
Molly e-mailed her clients offering a free 30-minute massage for referrals. In the following validation set of 100, Class 1 reflects the clients predicted to provide referrals and Class 0 reflects the clients predicted to not provide referrals. Based on the confusion matrix, what was the True Positive (TP) of current clients who provided referrals for a free massage?
TP = 18: There are 18 current clients who provided referrals that received a free massage that were correctly classified in the model.
Based on the following sensitivity results on constraints, how would an increase in machine hours impact the linear programming solution?
The hours can have an infinite increase without altering the solution. - Since the machine hours constraint is nonbinding, (implied with an Allowing Increase of 1E+30) an infinite increase can occur without altering the solution.
Modeling stage 4: Testing and Adjustment
The model is tested by gathering new data to check the accuracy of any prediction inferred from the analysis. If the predictions are not confirmed by the new evidence, the assumption...
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?
The range is between 4.111 and 5.75. - The objective coefficient is 5 with an allowable increase of 0.75 and decrease of 0.889 at the 300-unit level. Thus, between 4.111 and 5.75 range.
Calculus is the mathematics of change, and the primary tool for studying change is a procedure called differentiation.
True
If f(x) gets closer and closer to a number L as x gets closer and closer to c from both sides, the L is the limit of f(x) as x approaches c.
True
Informally, we might say "the quality of coffee is a function of its price". Here we are saying that price uniquely defines the quality of coffee.
True
Limits describe the behavior of a function near a particular point, not necessarily at the point itself.
True
Prescriptive analytics is the process of using decision analysis tools to improve decision making.
True
The average rate of change of function f on the interval [a,b] is the "slope" of a function between two points.
True
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.
True - When all other parameters are constant, the one unit change in the optimized value of an objective function is considered the shadow price or dual price.
The process of dividing a data set into a training, a validation, and an optimal test data set is called _____________blank.
data partitioning
The Daytona 500 runs 40 race cars. Of the 40, 19 cars crashed. This is a probability of 0.475 that a car will crash in the race. This is an example of which probability?
empirical - The event is observed with relative frequency of occurrence. The empirical probability is 19/40 of a crash occurring.
Mutually exclusive events
have joint probability of zero - Probability of the union is simply the sum of the two probabilities. P(A ∩ B) = 0.
In a linear regression, ε, read as epsilon, is
the random error - y = β0 + β1x1 + ɛ, where ɛ (the Greek letter read as epsilon) is the random error term.
The first step in performing linear programming is
to formulate a problem into a series of mathematical expressions.
The domain of a function is all real numbers such that the output of the function is a real number.
True
Sampson Limited 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?
6 Total Constraints - There are two constraints to demonstrate the capacity limit of machine 1 and machine 2 (Machine 1 time = 3p1 + 5p2 <= 500; Machine 2 time = 3p1 + 4p2 <= 500). There are 4 more constraints that show the minimum production level of each product in each month based on their demand (Month1 P1 demand = p1 <= 100; Month1 P2 demand = p2 <= 120; Month2 P1 demand = p1 <= 160; Month2 P2 demand = p2 <= 110).
Based on the following confusion matrix with a validation set of 100, Class 1 reflects the members targeted who purchased services and Class 0 reflects the non-targeted respondents who did not purchase services. Calculate the sensitivity rate.
62% - TP ÷ (TP + FN) = 18 ÷ (18 + 11) = 0.62 implying 62% of clients are identified correctly.
By viewing the following Excel snapshot, in Excel Solver what would be entered to formulate B11, Material (units) for Quantity?
=SUMPRODUCT(B2*B8) + (C2*C8)
Which of the following is NOT a goodness-of-fit measure?
Ans: simple regression model *The standard error of the estimate, the coefficient of determination, and the adjusted coefficient of determination are apart
Cross-Industry Standard Process for Data Mining (CRISP-DM) consists of six phases. Of the six, which one represents the phase where data wrangling occurs?
Data preparation - Data preparation is the phase that includes variable selection, data cleansing, and data wrangling.
As a manager, Mike uses linear programming to formulate a problem into a series of mathematical expressions. _____________blank refers to the choices or alternatives Mike selects to minimize or maximize the value of his goals.
Decision variables - Decision variables refer to the different choice or alternatives from which a decision maker has to choose to minimize or maximize the value of the goal or objective function.
Two events are __________blank if the occurrence of one event does not affect the probability occurrence of another.
Independent - Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event.
Sandra began collecting transaction details to see if the same items were in each sales transaction. Compute the matching coefficient and Jaccard's coefficient for pairwise transaction 1 & 2.
Matching Coefficient = 0.60 and Jaccard's = 0.50 - Matching coefficient 3/5 = 0.60 and Jaccard's coefficient = 2/(5 − 1) = 0.50.
Using the Manhattan distance between pairwise observations, which pairwise observation is most similar?
Observation 2 & 3 - Observations 2 & 3 are the most similar with the shortest distance at |6 − 8| + |4 − 2| = 4.
Graph: Y-axis = E(y) X-axis = x Line (bo) is straight going from low to high
Positive Linear - The slope parameter β1 determines whether the linear relationship between x and E(y) is positive (β1 > 0).
Based on the following sensitivity results on constraints, what is the optimal linear programming solution for Products 1 and 2?
Product 1: 300 units and Product 2: 150 units
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. 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.
Production Costs = 120x1 + 160x2 is the minimization function.
The break-even point happens where cost is equal to revenue.
True
