SQL & PL/SQL

I'm just getting acquainted with analytical functions. I like them. I'm having a problem, though. I want to sum up the results, but either I'm running into a limitation or I'm writing the SQL wrong. Any hints for me?

Hypothetical Table SALES consisting of a DAY_ID, PRODUCT_ID, PURCHASER_ID, PURCHASE_PRICE lists all the

Hypothetical Business Question: Product prices can fluctuate over the course of a day. I want to know how much per day I would have made had I sold one each of all my products at their max price for that day. Silly question, I know, but it's the best I could come up with to show the problem.

INSERT INTO SALES VALUES(1,1,1,1.0);
INSERT INTO SALES VALUES(1,1,1,2.0);
INSERT INTO SALES VALUES(1,2,1,3.0);
INSERT INTO SALES VALUES(1,2,1,4.0);
INSERT INTO SALES VALUES(2,1,1,5.0);
INSERT INTO SALES VALUES(2,1,1,6.0);
INSERT INTO SALES VALUES(2,2,1,7.0);
INSERT INTO SALES VALUES(2,2,1,8.0);

COMMIT;

Day 1: Iif I had sold one product 1 at $2 and one product 2 at $4, I would have made 6$.
Day 2: Iif I had sold one product 1 at $6 and one product 2 at $8, I would have made 14$.

The desired result set is:

DAY_ID                 MY_MEASURE
---------------------- ----------------------
1                        6
1                       14

The following SQL gets me tantalizingly close:

SELECT DAY_ID, 
  MAX(PURCHASE_PRICE) 
  KEEP(DENSE_RANK FIRST ORDER BY PURCHASE_PRICE DESC) 
  OVER(PARTITION BY DAY_ID, PRODUCT_ID) AS MY_MEASURE
  FROM SALES
ORDER BY DAY_ID
;

DAY_ID                 MY_MEASURE
---------------------- ----------------------
1                      2
1                      2
1                      4
1                      4
2                      6
2                      6
2                      8
2                      8

But as you can see, my result set is "longer" than I wanted it to be. I want a single row per DAY_ID. I understand what the analytical functions are doing here, and I acknowledge that I am "not doing it right." I just can't seem to figure out how to make it work.

Trying to do a sum() of max() simply does not work, nor does any semblance of a group-by clause that I can come up with. Unfortunately, as soon as I add the windowing function, I am no longer allowed to use group-by expressions (I think).

I am using a reporting tool, so unfortunately using things like inline views are not an option. I need to be able to define "MY_MEASURE" as something the query tool can apply the SUM() function to in its generated SQL.

(Note: The actual problem is slightly less easy to conceptualize, but solving this conundrum will take me much closer to solving the other.)

I humbly solicit your collective wisdom, oh forum.