Problem 1: Application of Maximum Flow (6 points) A project…

Problem 1: Application of Maximum Flow (6 points) A project manager needs to assign four critical development Projects \({\cal P} = \{P_1, P_2, P_3, P_4\}\) to three specialized Consultants \({\cal C} = \{C_A, C_B, C_C\}\). The technical compatibility between projects and consultants is known: \(P_1\) can be handled by \(C_A\) or \(C_B\). \(P_2\) can be handled by \(C_A\) or \(C_C\). \(P_3\) can be handled only by \(C_B\). \(P_4\) can be handled by \(C_A\) or \(C_C\). Each project must be assigned to exactly one consultant. The primary constraint is that each consultant can handle a maximum of two projects. Formulate a maximum-flow problem that determines whether it is possible to assign all four projects to the consultants, respecting both the compatibility and the consultant capacity constraints. Give a clear description of the flow network: a directed graph \(G\), a source \(s\), a sink \(t\), and a capacity function \(c\). Problem 2: Edmonds-Karp Algorithm (4 points) Consider the flow network \(G\) shown below. Your task is to perform the first iteration of the Edmonds-Karp algorithm.Draw the complete residual graph \(G_{f_1}\) that results after this first flow augmentation. Your graph should clearly label all nodes and the residual capacity of all remaining forward and new backward edges. Note: If multiple shortest paths of the same length exist, please choose the one that is lexicographically first, e.g., \(s \to a \to \dots\) before \(s \to b \to \dots\). Congratulations, you are almost done with this quiz.  DO NOT end the Honorlock session until you have submitted your work to Gradescope.  When you have answered all questions:  Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible.  Submit your PDF to Gradescope as follows: Quiz 12 Email your PDF to yourself or save it to the cloud (Google Drive, etc.).  Click this link to go to Gradescope to submit your work:  Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam.  End the Honorlock session. 

Consider the following problem: A cookie recipe calls for 23…

Consider the following problem: A cookie recipe calls for 23{“version”:”1.1″,”math”:”23″} of a cup of sugar, and you want to make 14{“version”:”1.1″,”math”:”14″} of the recipe. How much sugar do you need?  On your paper, (a) Write an annotated multiplication equation using the definition of multiplication to represent the cookie problem. (b) Use a clearly labeled strip diagram(s) or number line(s) to solve the cookie problem.  (c) Write complete sentence answer to question in the problem.   Click “Complete” when you have completed your work on this problem or are ready to move on. 

Both buttonwood and white mangrove are in the same plant fam…

Both buttonwood and white mangrove are in the same plant family and thus share many of the same characteristics. Identify a feature for each species that can be used to differentiate between them in the field. There is more than one feature that can be used, if you know a second feature, then you can write it in for extra credit. (3 points each)