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

question 12

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?

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Definitions:

Member Skills

Refers to the abilities and competencies that individual members of a group or organization possess, contributing to the collective effectiveness.

Improve

To make or become better through changes or modifications.

Cross-Functional Teams

Teams composed of members from different departments within an organization, working together towards a common goal.

Self-Leadership

The practice of leading oneself including setting personal goals, self-motivation, and self-directed behavior.