Cocalc Lesson 09 Ipynb

Watch the following video for a general introduction to integer programming. Decision variables constrained to integer values Can produce 5 or 6 cars, but not 5.72 cars For pure integer programming (IP) problems, solutions can be obtained simply by changing the domain for the LP from NonNegativeReals to PositiveIntegers in the Pyomo coding (as seen in textbook problem 3.4-10 as a... Computationally, integer programming can be much more difficult than linear programming (this post can help you visualize why this is so) Answer: e (read section 12.5 again if you missed this)

Answer: False (only one binary variable is needed) Answer: False (there are 2n2^n2n solutions, the number of solutions grows exponentially with the number of variables, see 12.5) By the end of this lesson, you will be able to: Use the SymPy library to perform symbolic computations, including basic algebraic manipulations, matrix manipulation, and calculus SymPy is a Python library that is used to make symbolic computations. It provides similar functionality as Mathematica, Maple, and Matlab, but with the advantage that SymPy is free.

Symbolic manipulation is not only used in research, but can be very helpful in your coursework to check theoretical calculations. This tutorial will give you a quick introduction to different functionalities of SymPy: Calculus of functions (differentiation and integration) CoCalc: Collaborative Calculations and Data Science For full credit, all code in this notebook must be both executed in this notebook and copied to the Canvas quiz where indicated. Reconsider the Wyndor Glass Co.

problem presented in Sec. 3.1. Management now has decided that only one of the two new products should be produced, and the choice is to be made on the basis of maximizing profit. Introduce auxiliary binary variables to formulate an MIP model for this new version of the problem. The original Wyndor model formulation using continuous variables is the following: d≤42w≤123d+2w≤18 \begin{array}{ccccc} d & & & \leq & 4 \\ & & 2w & \leq & 12 \\ 3d & + & 2w & \leq & 18 \end{array} d3d​+​2w2w​≤≤≤​41218​

Introduce auxiliary binary variables to formulate a mixed BIP model for this problem. Include a picture or LaTeX of the mathematical formulation. Let's look at the avocado data, which we looked at in week 3, and try to use the small hass volumes of avocados to predict their large hass volumes. To reduce the size of the dataset, let's also narrow our observations to only include avocados from 2015. We can measure the quality of our regression model using the RMSPE value—just like how we used accuracy to evaluate our knn classification models. In the readings, we looked at both RMSE and RMSPE and their differences.

RMSE refers to the root mean squared error, or predicting and evaluating prediction quality on the training data. RMSPE refers to the root mean squared prediction error, or the error in our predictions made about the actual testing data. We look at this property when we evaluate the quality of our final predictions. Let's look at the avocado data, which we looked at in week 3, and try to use the small hass volumes of avocados to predict their large hass volumes. To reduce the size of the dataset, let's also narrow our observations to only include avocados from 2015. We can measure the quality of our regression model using the RMSPE value—just like how we used accuracy to evaluate our knn classification models.

In the readings, we looked at both RMSE and RMSPE and their differences. RMSE refers to the root mean squared error, or predicting and evaluating prediction quality on the training data. RMSPE refers to the root mean squared prediction error, or the error in our predictions made about the actual testing data. We look at this property when we evaluate the quality of our final predictions. Recognize situations where a simple regression analysis would be appropriate for making predictions. Explain the kkk-nearest neighbour (kkk-nn) regression algorithm and describe how it differs from k-nn classification.

Interpret the output of a kkk-nn regression. In a dataset with two variables, perform kkk-nearest neighbour regression in R using tidymodels to predict the values for a test dataset. Using R, execute cross-validation in R to choose the number of neighbours. We often want our programs to take actions based on what's going on at the time (e.g. the current value of some variable). In a Python program, the if...elif...else statement is how we perform this sort of decision-making.

It allows for conditional execution of a line of code or a block of codes based on the value of the conditional expression. A conditional expression in Python is evaluated to a boolean, bool for short. A bool variable can take two values, True or False. Python implements all of the usual operators for bool logic using simple English words and, or, and not. We can check whether a variable of other data types (e.g. int, string, and even list) will be regarded as True or False using the bool() function.

Some of the results in the below examples (e.g. bool[""]) may not be what you think at first sight. Loosely speaking, for container data types like list, an empty state will be evaluted to False. in and is can be combined with not to form not in and is not Let's start with an illustrative example of the state of water based on temperature. So far we have looked at derivatives outside of the notion of differentiability.

The problem with this approach, though, is that some functions have one or many points or intervals where their derivatives are undefined. A function f is differentiable at a point c if lim⁡h→0f(c+h)−f(c)h exists.\begin{aligned}\lim_{h\to 0}{\frac{f(c+h)-f(c)}{h}}\text{ exists.}\end{aligned}h→0lim​hf(c+h)−f(c)​ exists.​ Similarly, f is differentiable on an open interval (a, b) if lim⁡h→0f(c+h)−f(c)h exists for every c in (a,b).\begin{aligned}\lim_{h\to 0}{\frac{f(c+h)-f(c)}{h}}\text{ exists for every c in (a,b).}\end{aligned}h→0lim​hf(c+h)−f(c)​ exists for every c in (a,b).​ Basically, f is differentiable at c if f'(c) is defined, by the above definition.

Another point of note is that if f is differentiable at c, then f is continuous at c.

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