Science:Math Exam Resources/Courses/MATH105/April 2017/Question 03/Statement

Use the method of Lagrange Multipliers to find the maximum value of the utility function $U=f(x,y)=16x^{\frac {1}{4}}y^{\frac {3}{4}}$, subject to the constraint $G(x,y)=50x+100y-500,000=0$, where $x\geq 0$ and $y\geq 0$. You do not need to justify your answer. Note that a solution that does not use the method of Lagrange Multipliers will receive no credit, even if the answer is correct.