Formula challenge - 2D lookup and sum

The problem

The data below shows cups of coffee sold at a small kiosk for a week at different hours of the day. The times in column B are valid Excel times. 

The challenge

What formula in cell I5 will correctly sum the total cups sold after 12:00 PM on Tuesday and Thursday? Relevant cells are shaded in green.

For your convenience, the following named ranges are available:

data = C5:G14
times = B5:B14
days = C4:G4

Download the Excel workbook, and leave your answer as a comment below.

Constraints

1. Your formula should dynamically locate the cells to sum, without hardcoded references. In other words, =SUM(D10:D14,F10:F14) is not valid.
2. Use named ranges when possible to make your formula easy to read.

Attachments 

 2D lookup and sum challenge.xlsx

HideAnswer (click to expand)

Many great answers! The most common approach was to use the SUMPRODUCT function like this:

=SUMPRODUCT(data*(times>0.5)*((days="Tue")+(days="Thu"))) 

Where the expression (times>0.5) is equivalent to:

=(times>TIME(12,0,0))

This works because Excel handles times as fractional values of 1 day, where 6:00 AM is 0.25, 12:00 PM is 0.5, 6:00 PM is 0.75, etc.

If SUMPRODUCT used this way is new to you, this formula is based on the same idea, and includes a full explanation. SUMPRODUCT may seem intimidating, but I encourage you to give it a try. It is an amazing tool.

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