90-722: Management Science I, AFTERNOON SECTION Midterm, Spring 2017Do not turn the page until you are told to do so. Write your answers below each question.Note how much each problem is worth and budget your time. Total points possible: 100Name: ______________________________Q1: _________ out of 8 possible pointsQ2: _________ out of 12 possible pointsQ3: _________ out of 15 possible pointsQ4: _________ out of 12 possible pointsQ5: _________ out of 20 possible pointsQ6: _________ out of 12 possible pointsQ7: _________ out of 12 possible pointsQ8: _________ out of 9 possible pointsTotal Possible Points: 1001Question #1: (8 Points): I created a “division” table showing how various fractions convert to percentages. Show how the (“world’s worst”) dialog box was filled in to get Excel to complete that table.2Question #2: (12 Points): a) How many decision variables and constraints (besides non-negativity) are there in a standard assignment problem that assigns 10 people to 10 tasks? b) Consider a slight variation of the standard make vs. buy problem in which there are 4 constrained resources in one’s own factory and each of the five products can be made in-house or ordered from either of two distinct suppliers. How many decision variables and how many constraints (besides non-negativity) would there be?c) Suppose you solved a max flow problem as a transshipment problem using the trick we discussed in class, maximizing the flow from Node #1 to Node #20 in a network with 25 nodes and 100 arcs. How many decision variables and how many constraints (besides non-negativity and simple upper bounds) would there be in that formulation? 3Question #3: (15 Points): I’ve pasted below the graphical solution to a standard two-variable product mix problem whose objective function is Max Z = X1 + X2. a) What is the optimal solution?b) Which constraints are binding?c) What would Z* be if the objective function coefficient on X1 increased to 3?d) Add to the diagram a redundant constraint.e) What is the reduced cost on variable X1? (in the original diagram)4Question #4: (12 Points): Recall that in HW #1, Problem #6, Howie’s friend Harold convinced Howie to commit to selling at least 45 “Super Bowl” kits that do-it-yourselfers (DIY) can assemble at home. I’ve pasted the spreadsheet from the optimization problem below.a) What type of problem is this?b) What is the solution and solution value?c) What constraints are binding?d) What does the 12 in Cell B9 mean? 5Question #5: (20 Points): Write the algebraic formulation of the LP in the previous problem.6Question #6: (12 Points): I’ve printed the sensitivity report for this problem below. Use it to answer these questions.a) For what range of objective function value coefficients on Aqua Spas is the current solution optimal?b) For what range of amounts of tubing would the nature of the solution remain the same?c) If Howie could acquire 100 more pumps, how much should they be willing to pay for that additional resource?d) If Howie had to sell one Hydrolux, what would the total profit be then? 7Question #7: (12 Points): I ran a solver table to explore the implications of how the solution and solution value of this LP depends on the amount of tubing available.a) What does the 30 under the Hydrolux column mean?b) Why is the first line of the table blank?c) What is the shadow price for tubing when there is between 3000 and 3200 feet of tubing available?d) Write a sentence or two explaining how the number of Aqua Spas depends on the amountof tubing that is available and why that makes sense. [Write neatly. If your answer is hard to read, it won’t be graded.] 8Question #8: (9 Points): Draw the network diagram corresponding to this transshipment problemthat is implemented in the node-arc incidence approach in Excel. Label arcs with their costs. Putthe node’s ID number inside its circle and put the associated demand or supply (if any) in a box next to the
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