73-220Quantitative Decision Models I

Assignment #12006 Fall Term

Due Date: Monday, September 25, 200610:00am for Section 17:00pm for Section 30

Instructions: 1. For Question 2.13, use the graphical technique to find the optimal solution. Clearly

label your coordinates, constraints, feasible region, and all corner points. It is NOT required to use computer drawing.

2. For Questions 2.27 and 2.53, linear programming mathematical formulations are to be provided in terms of decision variables (including units), objective function (max or min), and constraints (preferably with appropriate labels). Either Excel solver or Management Scientist can be used to solve these models. You are required to submit the SOLVED sheets (either Excel or Management Scientist) to support your answers. Graphical solutions are NOT required for these two questions.

3. For Question 4, you may use either algebraic, graphical, or Excel spreadsheet approach to formulate and solve the problem.

4. All the question numbers refer to our required textbook, Anderson, Sweeney, and Williams, An Introduction to Management Science: Quantitative Approaches to Decision Making, 11th Edition, South-Western, 2005. If you use an earlier edition, it is your responsibility to make sure that you work on the right questions.

5. Assignments are to be collected during the first 10 minutes of the class on September 25, 2006, i.e., up to 10:10am for the morning class or 7:10pm for the evening class. Late assignments up to the end of the class will be accepted with a 30% late penalty. Any submission beyond this time window will not be accepted. You must hand in your assignment to the section that you officially registered.

6. Assignments must be stapled and put inside a sufficiently large envelope with your student ID number, name, course title and number, and assignment number on it.

Q2.13 on page 72Q2.27 on page 76Q2.53 on page 82-83

Q4. When Molly Lai purchased the Clean Clothes Corner Laundry, she thought that because it was in a good location near several high-income neighbourhoods, she would automatically generate a good business if she improved the laundry’s physical appearance. Thus, she initially invested a lot of her cash reserves in remodeling the exterior and interior of the laundry. However, she just about broke even in the year following her acquisition of the laundry, which she did not feel was a sufficient return given how hard she had worked. Molly didn’t realize that the dry cleaning business is very competitive and success is based more on price and quality service, including quickness of service, than on the laundry’s appearance.

In order to improve her service Molly is considering purchasing new dry cleaning equipment, including a pressing machine that could substantially increase the speed at which she can dry clean clothes and improve their appearance. The new machinery costs $16,200 and can be financed as an equal monthly payment of $450.00 for three years. Molly estimates her variable costs to be $0.25 per item dry cleaned, which will not change if she purchases new equipment. Her current fixed costs are $1,700 per month. She charges customers $1.10 per clothing item.

a. What is Molly’s current monthly volume?b. If Molly purchases the new equipment, how many additional items will she have

to dry clean each month to break even?c. Molly estimates that with the new equipment she can increase her volume to

4,300 items per month. What monthly profit would she realize with that level of business during the next three years? After three years?

d. Molly believes that if she does not buy the new equipment but lowers her price to $0.99 per item, she will increase her business volume. If she lowers her price, what will her new break-even volume be? If her price reduction results in a monthly volume of 3,800 items, what will her monthly profit be?

e. Molly estimates that if she purchases the new equipment and lowers her price to $0.99 per item, her volume will increase to about 4,700 units per month. Because of the local market, that is the largest volume she can realistically expect. What should Molly do?