Management Science

Assignment 1

Due: Beginning of class on 1/21/2010

Guidelines for Submission: Late HW will not be accepted. All the working has to be shown on the homework. Turn in a hard-copy of your work at the beginning of class on 1/21/2010. Provide clear and complete definition of decision variables. Write down all constraints and explain the constraints. Whenever you use Excel, turn in a hard-copy of the Answer and Sensitivity reports.

PROBLEM 1:

Solve the advertising problem mentioned in Chapter 2, Problem 6 using LP. Use Graphical Method to solve this problem.

Solution:

Notice how the problem states linearity assumption in number of ads placed. This decision is with management team on how it interprets the fractional solutions like 3.5 ads. But sometimes, as we will see in next topic “Integer Programming”, this interpretation does not hold ground.

Decision Variables

• X = Number of weekday ads placed by PMA in month of August

• Y = Number of Sunday ads placed by PMA in month of August

Objective Function

• Maximize Total Exposure

Constraints

• Total advertising Budget

• Minimum number of ads to be placed in weekdays

• Minimum number of ads to be placed on Sundays

• Maximum number of weekdays that exist in August

• Maximum number of Sundays that exist in August

• Non-negativity

Writing out everything in simple words like above, for yourself can help you in doing the mathematical part of formulation easy.

Part (a)

LP Formulation

Maximize 30000X + 80000Y

Subject to

2000X + 8000Y = 8 (Minimum of 8 weekdays)

Y >= 2 (Minimum of 2 Sundays)

X = 0

Truly speaking, if same person sees the ad in weekday and that same person also sees the ad on a Sunday, then total exposure should be counted as only once unlike the double counting we do in this formulation. This situation is quite possible in reality where in, a person subscribes to the same newspaper for the entire week. However, in this formulation we neglected...