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- A.cost/cps + B.cost/(cps+A.cps) < B.cost/cps + A.cost/(cps+B.cps)
- A.cost/cps - A.cost/(cps+B.cps) < B.cost/cps - B.cost/(cps+A.cps)
- (A.cost(cps+B.cps))/(cps(cps+B.cps)) - (A.cost*cps)/(cps(cps+B.cps)) < (B.cost(cps+A.cps))/(cps(cps+A.cps)) - (B.cost*cps)/(cps(cps+A.cps))
- (A.cost(cps+B.cps)-A.cost*cps)/(cps(cps+B.cps)) < ((B.cost(cps+A.cps)-B.cost*cps)/(cps(cps+A.cps))
- A.cost*B.cps/(cps(cps+B.cps)) < B.cost*A.cps/(cps(cps+A.cps))
- A.cost* B.cps * cps(cps+A.cps) < B.cost* A.cps * cps(cps+B.cps)
- A.cost * cps(cps+A.cps)/A.cps < B.cost * cps(cps+B.cps)/B.cps
- now that the A and B variables are separated we can just take the first part and voila
- A.cost * cps(cps+A.cps)/A.cps
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