The Charming City Data Analytics Company is considering six projects for the next month. The number of data analysts and the number of support personnel required for each project, and the expected profit for each project are given below.

Project

1 2 3 4 5 6

______________________________________________________

Data Analysts Required 3 3 4 4 5 4

Support Personnel Required 3 3 4 5 4 4

Profit (in thousands of dollars) 220 290 220 180 320 260

Formulate a capital budgeting problem that maximizes the company's total profit subject to the following constraints:

- Use no more than 20 data analysts

- Use no more than 22 support personnel

- If project 2 is done, then project 1 must be done and vice versa

- At least four projects must be selected

(a) Define the decision variables.

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. What does each constraint represent?

Note: Do NOT solve the problem after formulating.