Bus Final Trinity

Minimization

cost, time, distance

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?

decreases by 15 units

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

Events are considered __________blank if they include all outcomes in the sample space.

exhaustive

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

false

For a function f(x) that is not linear, the rate of change is constant and conforms with x.

false

If the function f is differentiable at x=c, then f is increasing at x = c if f'(c) <0

flase

stage one formulation

given a real world situations

subjective probability

is the individual's personal estimate of the chance of loss

In a linear regression, ε, read as epsilon, is

the random error.

Exclusive

they both can not occur at the same time

The first step in performing linear programming is

to formulate a problem into a series of mathematical expressions.

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

SEMMA

Sample, Explore, Modify, Model, and Assess

exhaustive

that one of them must occur

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

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 process of applying a set of analytical techniques for the development of machine learning and artificial intelligence is called data mining.

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

The average rate of change of function f on the interval [a,b] is the "slope" of a function between two points.

true

stage two: analysis of the model

we use mathematical

predictive analytics

what could happen

descriptive statistics

what has happened

prescriptive analytics

what should we do?

Exhaustive events

All possible outcomes of an experiment belong to the events. Include all outcomes in the sample space.

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

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

Based on the following table, what is the sample regression equation?

Earnings = 10,004.9665 + 0.4349Cost + 178.0989Grad + 141.4783Debt

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

The revenue is obtained from selling x units at unit price p(x) is the total cost divided by the number of units produced.

Now this would be false

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

The break-even point happens where cost is equal to revenue.

True

The domain of a function is all real numbers such that the output of the function is a real number.

True

The process of computing the derivative is called differentiation

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

artificial intelligence

Type of software that can process information on its own without human intervention.

domain

all real numbers such that the output of the function is a real number.

Stage three: interpretation

any conclusion that

classical probability

based on logical analysis

empirical probability

calculated as a relative frequency of occurrence

The process of dividing a data set into a training, a validation, and an optimal test data set is called _____________

data partitioning

Mutually exclusive events __________

have joint probability of zero

Two events are __________blank if the occurrence of one event does not affect the probability occurrence of another.

independent

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.

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

parameters

maximization

profit, revenue, return

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

random

Which of the following is not a goodness-of-fit measure?

simple regression model

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 _____________blank to make the observations unit-free.

standardizing

What is the probability when a personal assessment is made without referencing data?

subjective probability

break even point

the point at which the number of units sold is equal to revenue

complement rule

the probability that an event does not occur is 1 minus the probability that the event does occur

linear programming

the process of finding the maximum or minimum values of a function

Calculus is the mathematics of change, and the primary tool for studying change is a procedure called differentiation.

true

funciton

A relation where every input (x) has only one output (y)

This represents which relationship?

Positive linear

Stage four: testing and adjusting

The model is tested by

mutually exclusive events

Events that cannot occur at the same time.