M1D2 RQ

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School

University of Michigan *

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Course

301

Subject

Industrial Engineering

Date

Jan 9, 2024

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Pages

1

Uploaded by CommodoreCaribouMaster1044

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Question 1 1/1pts Which of the following best describes the solution to the LP with the objective min x + y with the constraints x +y >= 5,y >=2, x >=0. Unbounded feasible region with only one optimal solution (X)Y) = (3,2). Unbounded feasible region with no optimal solution. Unbounded feasible region with multiple optimal solutions. Infeasible, no solution. A first step is to visualize or draw the feasible region. It is unbounded because x and y can take any value as long as they sum to greater than 5 where x is non-negative and y is at least 2. Next, you can think about the z-line. The slope of the z-line is -1. And the slope of the first constraint is -1. The direction of minimization of the objective function is towards Constraint 1. They will be co-incident, creating multiple optimal solutions on the line between (X)Y) = (0,5) and (X)Y) = (3,2). 1/1pts Question 2 In Excel, you solve a profit-maximizing LP with two variables X and Y. Solver finds the optimal solution and you see a value of 9 in the X solution cell and 2 in the Y solution cell. You have a resource that is required for making both X and Y. Every unit of X variable uses up 2 units and every unit of Y uses up 3 units of your resource. How much of your resource have been used at the optimal solution? » . Plug in the values of X and Y in 2X+3Y to find the correct answer. Question 3 0/1pts In a linear program with two decision variables, X and Y, which of the following is NOT possible? m[ Having an unbounded feasible space but a unique optimal solution. \swer Having exactly two optimal solutions with different (X,Y) values. Having an infeasible problem. Having infinitely many (multiple) optimal solutions. | | In an LP, if we have multiple optimal solutions, we have infinitely many of them. If there are two corner solutions that are optimal, all points connecting those two solutions are also optimal. It is possible to have a unique optimal solution (or even multiple optimal solutions) for an LP with an unbounded feasible space if the objective function does not improve in the direction of unbounded region. An over-constrained LP can be infeasible.
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