a) Develop a mathematical model formulation for the problem of minimizing the total cost of completing the project (Clearly define the decision variables you use. Write down the objective function and the constraints explicitly, not in closed form).

b) Use an optimization package to find the solution, report and explain the solution (You need to provide the corresponding file(s)).

c) Repeat parts a and b assuming that partial crashing is not allowed.

The following data were obtained from a study of the times required to conduct a consumer test panel study (Costs are given in thousands of dollars, time in weeks): Indirect cost is made up of two components: a fixed cost of $5,000 and a variable cost of $1,000 per week of elapsed time. Also, for each week that the project exceeds 21 weeks, an opportunity cost of $2,000 per week is assessed. Assuming that partial crashing is allowed