A Company Estimates That Its Annual Profits for Next Year $z = 6 x y - y ^ { 3 } - x ^ { 2 }$

Essay

A company estimates that its annual profits for next year will be $z = 6 x y - y ^ { 3 } - x ^ { 2 }$ , where $x$ represents investment in research and $y$ represents investment in labor. All units are in tens of thousands of dollars. Determine the amount the company should spend on research and on labor to maximize its profit. What is maximum profit?