A consulting firm has four projects to consider. Each project will require time $($in days$)$ in the next three months according to the table below.

$\backslash$table$[[$Project$,$Time in first month,Time in second month,Time in third month,Revenue$],[$A$,5,8,6,40000],[$B$,6,7,7,28500],[$C$,8,7,6,42400],[$D$,6,7,3,25500]]$

Revenue from each project is also shown. There is $22$ days' time available in the first month, $24$ days' time available in the second month, and $20$ days' time available in the third month to do these projects. The I management wants to select at least $3$ projects. If project $B$ is selected, then project $C$ must also be selected. The objective of the firm is to maximize the total revenue.

Formulate a capital budgeting problem for the above situation by determining

$($a$)$ The decision variables for this problem.

$($b$)$ The objective function for this problem. What does it represent?

$($c$)$ All the constraints for this problem. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.