Here's the formula:
=SUM((C31:C46)*(E31:E46))-SUM((C47:C51)*(E47:E51)/2)+SUM((C54:C59)*(E54:E59))+SUM((C67:C71)*(E67:E71 ))

My guess is that these are matrices being multiplied together and matrix
algebra is different than straight multiplication. So, Excel requires
CTRL+SHIFT+ENTER to tell its calculation enginge to do matrix
multiplication....

Am I correct here?

Also: it seems to me that the same calculation can be done with SUMPRODUCT.

Dave

--
Brevity is the soul of wit.