### Sensitivity Analysis and Optimization Problem#### Problem 4Reconsider the model from Problem 3 with the objective function:\[\text{Maximize } Z = c_1 x_1 + c_2 x_2\]where $ c_1 \geq 0, c_2 \geq 0 $. Use sensitivity analysis on the objective coefficients to answer the following questions:(a) Find the range of $\frac{c_1}{c_2}$ such that the optimal solution remains as $(x_1^*, x_2^*) = (3,4)$.(b) Find the range of $\frac{c_1}{c_2}$ such that the optimal solution remains as $(x_1^*, x_2^*) = (4,2)$.(c) Find the range of $\frac{c_1}{c_2}$ such that the optimal solution remains as $(x_1^*, x_2^*) = (0,5)$.(d) If $ c_1 $ and $ c_2 $ are allowed to be negative, find the conditions on $ c_1 $ and $ c_2 $, and the range of $\frac{c_1}{c_2}$ such that the optimal solution remains as $(x_1^*, x_2^*) = (4,0)$.#### Question 3Given as follows:Consider the following problem:\[\text{Maximize } Z = 3x_1 + 2x_2,\]subject to:- $ x_1 \leq 4 $ (resource 1)- $ x_1 + 3x_2 \leq 15 $ (resource 2)- $ 2x_1 + x_2 \leq 10 $ (resource 3)- $ x_1 \geq 0, \, x_2 \geq 0, \, x_3 \geq 0 $.The optimal solution is $(x_1^*, x_2^*) = (3,4)$ with $ Z^* = 17 $.(a) Is any of these three constraints a binding constraint?(b) Use graphical analysis to determine the shadow prices for the respective resources

Note: - Since the exact question that has to be answered is not specified we will answer the first…

Answered: 4. Reconsider the model in Problem 3…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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