This is a longer one but I'll make sure to upvote and rate! There are three plants that manufacture shoe, two distribution centers, and five warehouses. We need to ship the shoes to the warehouses at a minimum cost satisfying the constraints outlined in the spreadsheet. Namely, each plant can only produce so much product, the amount of shoes passing through the distribution centers has to remain constant (in has to equal out), and each warehouse has a minimum amount that they need in order to satisfy demand. The data are given in the Excel file below. Code each problem 1-7 in python using the excel sheet information and the beginning of the python code. Code each question separately.

1. What is the minimum cost to ship these boots from our plants to the warehouses while satisfying all of our constraints? 2. What are the final values of the decision variables? 3. Is there any slack in the system? If so, what is the amount/route that shows slack? 4. Suppose management tells us that the per unit shipping cost from Plant P3 to Distribution Center D1 is going to change to $.60. How do your answers to 1 . and 2. change? 5. Show the values of the decision variables as barcharts using seaborn. Create a separate plot for Plants to Distribution Centers (colored by DCs) and another for DCs to Warehouses (colored by WHs). 6. Create a sequence of shipping costs ( P3 to D1 ) from 0.5 to 0.7 in one cent increments (21 unique values). a. Make a plot showing how the overall shipping costs change as a function of this sequence. b. Make two plots showing: (1) the amount of boots shipped between Plant P3 and the two distribution centers and (2) the amount of boots shipped between each distribution center and the five warehouses. The lines be shown using different colors. 7. Finally, let's investigate how changing the demand on the third warehouse changes the final value of the objective function. Create a sequence of demands from 4700 to 7000 by 100 units. Plots those demands on the x axis and the final minimum cost on the y. Back to Top Import Modules import pandas as pd import pyomo.environ as pe import matplotlib.pyplot as plt import seaborn as sns Read and convert data \begin{tabular}{|l|l|r|r|r|r|} \hline Data & (To) Distribution Center \\ \hline & (From) Plant & D1 & \multicolumn{1}{|l|}{ D2 } & \multicolumn{1}{l|}{ Capacity } \\ \hline P1 & 0.5 & 0.6 & 10000 \\ \hline P2 & 0.65 & 0.65 & 11000 \\ \hline P3 & 0.63 & 0.78 & 10500 \\ \hline \end{tabular} (To) Warehouse Objective: Minimize total shipping cost Stage 1 Stage 2 Total \begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hlinex12 & x13 & x23 & x32 & x24 & x42 & x26 & x35 & x53 & x45 & x54 & x46 & x56 \\ \hline \end{tabular} Node 1 Node 3 Node 4 Node 5 Node 6 \begin{tabular}{|r|r|r|r|r|r|r|} \hline 1 & 1 & & & & \\ \hline & & 1 & 1 & 1 & 1 & 1 \\ \hline & 1 & 1 & 1 & & & \\ \hline \end{tabular} 0