I would suggest that whoever suggested you can optimise any single page for 15 keywords is kidding themselves or you. 3 - 5 keyword / key-phrases is your most likely choice and even ten it takes concerted effort, time and patience.

I would suggest that if you need to optimise on 15 keywords split your page into say 3 or 5 separate pages on focus on 3 - 5 keywords on each page.

Consider the statistics - if the ideal page is 400 - 700 words, your optimum density is 3% - 5% and you also need the page to be readable and make sense then with 15 keywords you just not going to cut it.

The basic principals of optimising for page rankings that whatever you do it must be focused and you must be prepared to change whatever you have done.

Another factor you need to take into account is what the keywords are and what the degree of competition is on these words. Gaining page #1 ranking on "financial planning" for instance is going to be a very hard task!

Your best opportunity for lifting rankings is through off-page optimisation.

Only other answer is to invest big money in AdWords campaigns