There are three resource types available for a certain project. One unit of each resource type is available. The project manager wants to evaluate the project cost on the basis of how resource teams are made up. She has the option of using a resource team, where the team can consist of only one resource type or a combination of resource types. If the team consists of more than one resource type, the resources will start and stop working at the same time. Fractions of a workday are permissive with prorated cost.

Resource 1 can complete the project alone in 50 days at a cost of \(\$ 2,500 /\) day.

Resource 2 can complete the project alone in 35 days at a cost of \(\$ 5,750 /\) day.

Resource 3 can complete the project alone in 75 days at a cost of \(\$ 1,500 /\) day.

The resources produce identical quality of work.

a. Determine the team composition that will yield the minimum project cost.

b. What is the project duration corresponding to that minimum cost? Plot all the project costs versus the respective project durations.