What formula am I using for this problem? I don\'t want the problem solved, just

Question

What formula am I using for this problem? I don't want the problem solved, just a little guidence and rationale on the formula used.

Penny has $10,000 to invest. She is considering a certificate of deposit (CD) that is expected to yield 5%, a mutual fund expected to yield 7%, and stocks expected to yield 9%. The amount invested in the mutual fund can be no more than the amount invested in the CD and stocks together. The amount in the mutual fund and stocks must be no more than $8000. How much should Penny invest in each investment vehicle to maximize her total expected yield?

Thanks!

Explanation / Answer

p=x*1.05 + y*1.07+ z*1.09

p=x*1.05 + y*1.07+ (10000-(x+y))*1.09

y<(x+10000-(x+y))==>y<5000

y+z<8000

y+10000-(x+y)<8000==>x>2000

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