Question: Find the optimal value of the function

\[f\left( x,y \right)=3.5{{x}^{2}}+{{y}^{2}}-42x-28y+5xy+190\]

subject to

\[6x+5y=37\]

Use the second order condition to determine if the optimal point is maximum or minimum. What is the optimal value of the function if the constant in the constraint increases from 37 to 39 units?

Repeat using EXCEL and confirm that you get the same result for the optimal values of \(x,y,\lambda \) and f (x*, y*). Be careful to explain how you use the spreadsheet functions to obtain your solution.