Management Science

This homework assignment must be prepared individually and submitted online through Brightspace. You may submit the assignment multiple times but only the last submission will be graded. See the Syllabus for more information on Homework requirements and expectations. Any necessary modifications to this assignment will be posted to Brightspace.

**Due Date:** Saturday, November 4, 2023

**Time**: 11:59pm

**Compile your answers in Microsoft Excel and submit one file. Each problem should be on a separate worksheet. Do not put multiple homework problems on one worksheet.**

**Problem 1 **(30%): Chapter 1** – **Question 6. Only formulate and do not solve. Place the formulation in a textbox. Remember to include labels for constraints.

**Problem 2 **(30%): Chapter 3** – **Question 1. Ignore Part a of the problem that asks to solve graphically. In fact, do not solve this problem at all or answer the questions in Part a. Just formulate the linear program in a textbox and remember to include labels for all constraints.

Note: There is a typo in the last sentence of the problem description. Change the last sentence to be, “…and quality checking is at most 90 hours.”

**Problem 3 **(40%)**: **Chapter 3** – **Question 3, Parts a and b. Note, an “extreme point” is the intersection of two constraints and are the corner points for the feasible region shape. __Do not replicate the graph in this problem in your Excel worksheet__. Just answer the following questions.

Complete Parts a and b as written in the textbook. Then, complete the questions below.

c. What is the objective function value for the objective function line through the point (1,3)? (Another name for the objective function line is “isoprofit line,” see page 24 in the textbook for a description.)

d. What is the objective function value for the objective function line through the point (2,5)? Is this an improvement to the answer in part c?

e. Which best describes the linear program (LP): infeasible, unique optimal solution, alternate optimal solution, or unbounded optimal solution? Why?

f. Consider the following change to a constraint: Due to hotter than normal temperatures, two acres of land have been deemed unusable for these crops.

· Will the original feasible region stay the same, increase, or decrease?

· Will the optimal value stay the same, increase, or decrease?

· If the constraint change does cause the optimal solution and optimal value to change, what are the new optimal solution and optimal value?

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