Multiple If AND criteria formula help

Hi,

I need a formula that will:
1) perform one calculation if a nearby cell (E31) is blank (if blank, then cost * markup)
2) Perform another calculation if it is populated and a second cell says "T&M" (if populated and "T&M, then takes the labor sell rate ($65) and multiplies by the quantity entered (E31)
3) Perform another calculation if it is populated and a second cell says "Estimate" (if populated and "Estimate" then takes labor cost rate and multiplies it by the MU (1.7) (F6) and multiplies that by the quantity entered (E31).
4) Remain blank if quantity is 0 and nothing is entered into the cost cell (I31)

I loaded the "experimental" workbook below."v3.3"

This calculation is more complicated that I can solve on my own, so I'm asking for help.

Thanks,

-Rod

Thanks for taking time Tsjallie.
This is super close, but is not capturing the cost when I enter it into column I.
It needs to be able to either capture the HOURS COST in the cost field (based on the hours I enter in column E), or the MATERIALS cost based on the dollars I manually enter it into column I.
I want to be able to just grab the anchor and drag down so the entire column (J) can accomplish those tasks. Rather than having to enter one calculation in J in the hours rows and another in the materials rows.

Does that make sense?

Also, Column G does nothing functional. I should have deleted it before posting.
The real MU shows up in F6.

Awesome!

It works!

Thank you, thank you, thank you, thank you.