Project A profitablity index $1\mathrm{.}21$

Project B profitability index $1\mathrm{.}14$

Project C profitability index $1\mathrm{.}17$

Project A NPV $$34,380\mathrm{.}17$

Project B NPV $$44,049\mathrm{.}59$

Project C NPV $$26,942\mathrm{.}15$

$($a$)$Suppose these three projects are independent. Which project$($s$)$ should the company accept based on the profitability index rule?

$($b$)$Suppose these three projects are mutually exclusive. Which project$($s$)$ should the company accept based on the profitability index rule?

$($c$)$Suppose the budget for these projects is $$470,000.$ The projects are not divisible. Which project$($s$)$ should be accepted?