A firm has contracts with two marketing companies, Simon and Associates and East First, to which it outsources its marketing. The firm currently has four products close to release. Each product requires a marketing plan. For each product, the firms policy is to select one outsourcing company to develop the marketing plan for that product. It wants to minimize the cost of the marketing plans in total.

The following table summarizes the consultancy fees quoted by the two marketing companies for each of the proposed marketing projects. The fees are in $10,000s. In order to fulfil the terms of its contracts with the two marketing companies, the firm must offer at least one of the four projects to each company. East First has a busy backlog of existing work and could not accept more than two new projects.

Project 1 Project 2 Project 3 Project 4 Simon and Associates 13 9 10 30 East First 11 6 6 22

Your task is to solve the problem using linear programming. Assume fractional values of variables are feasible. Write answers to the following questions in the spaces provided.

1. Define all decision variables. Make sure to indicate the units of variable values.

2. Write an objective function and explain its meaning briefly.

3. Write all constraints and explain their meaning briefly.

4. Create a model of the problem in Excel and solve it using Excel Solver. Put your 3 name and ID in the filename. Save the Excel file. After completing the whole exam and submitting the exam paper to a proctor, upload the Excel file on Moodle. Do not open an internet browser before you have submitted your exam paper.

5. Write the optimal solution and the optimal objective function value that were deter- 3 mined by the Excel Solver. Write an interpretation of the optimal solution.

6. Based on the sensitivity report, write whether the optimal solution would change if 3 the fee of Simon and Associates for Project 2 increased to 11. Explain your answer briefly. What effect would it have on the optimal objective function value?

7. Using the sensitivity report, write how the optimal objective function value would 3 change if East First could accept only one new project. Explain your answer briefly. Would this change affect the optimal solution?

8. Write a linear constraint to ensure that the amount of fees that the firm pays to 3 Simon and Associates is at most 50% of the total fees that it pays for all projects. Decide without using Excel Solver whether the optimal solution would change or stay the same if this constraint were added to the model. Explain your answer briefly.

9. The firm decides that whichever marketing company develops the plan for Project 1 3 should also develop the plan for Project 3. Write below all necessary modifications of your mathematical model. Make sure that your model is linear. (Note: You do not have to implement the modified model in Excel.)