MGMT 306: Management ScienceFall 2020

HOMEWORK ASSIGNMENT1

Homework assignment must be prepared individually and submitted online through Brightspace.You may submit the assignment multiple timesbut 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:Friday, September 4, 2020

Time: 5:00pm

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.Remember to include labels for constraints.

Problem 2(30%):Chapter 1-Question 8. Only formulate and do not solve.Remember to include labels for constraints.Ignore the constraint about automobiles compromising 2/3 of the entire fleet.

Hint: For formulation problems (like Questions 1 and 2), I recommend using a textbox on separate worksheets for your answers. They are easy to read and will help the graders.

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 (0,3)? (Another name for the objective function line is "isoprofit line," see page 32 in the textbook for a description.)

d.What is the objective function value for the objective function line through the point (3,3)? 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?

f.Consider the following new constraint: The water filtering had to be replaced. The new system will only be able to provide water to a maximum of seven acres of tomatoes. Pepper production is not affected.

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

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

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