Profit question

Please refer to the attachment.

??

Just edited - with the attachment

We just need to consider the lost profit which is related to the waste.

Shouldn't they say "lost revenue" as "lost profit" to me means find the lost revenue and exclude the cost to get the lost profit?

The long winded explanation shows this is correct, i.e. the lost profit.

However the short solution misses out an explanation. Let P, Pa, S and C be the theoretical profit, actual profit, theoretical sales and cost respectively. Then
Pa = 0.77S - C
So this is the profit on what the store sells.
P = S - C
This is the theoretical profit.
Subtract the two gives
P-Pa = 0.23S
It looks like revenue as it only depends on sales, but it is the lost profit. The production cost information is subtracted out.

Perfect. Thank you!
I didn't recognize it was the same thing until you showed it algebraically. Without the proof, I find it difficult to see how the selling price x no. of wasted items = lost profit, so I guess I would be forced to do it the long way?

Perfect. Thank you!
I didn't recognize it was the same thing until you showed it algebraically. Without the proof, I find it difficult to see how the selling price x no. of wasted items = lost profit, so I guess I would be forced to do it the long way?

The "obvious" way of looking at it is that you've already spent the money on priduction, so any revenue gained from selling "waste" is pure profit. Therefore the profit difference is the revenue gained from selling the wastage.

Obviously, this "obvious" is an hour or so later.