Question $3-$ You are managing two projects simultaneously with the following details:

Project A: Requires $10$ resources for $5$ weeks with a revenue of $$50,000.$

Project B: Requires $8$ resources for $4$ weeks with a revenue of $$40,000.$

Resource availability: $12$ total resources per week.

Penalty for delay: $$1,000$ per week per project.

Your goal is to allocate resources dynamically to maximize total revenue while minimizing penalties for delay.

Which combinations of methods best solve this problem?

Options:

A$.$ Develop a linear programming model to allocate resources across projects while minimizing penalties.

B$.$ Use a dynamic programming approach to allocate resources optimally each week.

C$.$ Apply sensitivity analysis to test different resource allocations and their impact on revenue.

D$.$ Formulate a mixed$-$integer programming model to account for resource constraints and penalties.

E$.$ Use heuristic$-$based resource allocation combined with Monte Carlo simulation to test outcomes.