A financier plans to invest up to $$500,000$ in two projects. Project A yields a return of $12\%$ on the investment of $x$ dollars, whereas Project $B$ yields a return of $17\%$ on the investment of $y$ dollars. Because the investment in Project $B$ is riskier than the investment in Project $A,$ she has decided that the investment in Project $B$ should not exceed $40\%$ of the total investment. How much should the financier invest in each project in order to maximize the return on her investment?

$(x,y)=()$

What is the maximum return?

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