I'm taking an economics course this summer, and while multivariable calculus is not required (Calc 1/2 are), the professor will explain how to use a couple multivariable concepts.
Ex: $F\left(x,y\right)=11+\left(y-14\right)+2x\:and\:the\:constraint\:is\:12\ge x+y$ I Want to maximize the function, so I will say 12=x+y.
Using the Lagrange method, my textbook says: $L\left(x,y,\lambda \right)=F\left(x,y\right)+\lambda \:g\left(x,y\right)=11+y\left(12-y\right)+2x+\lambda \:\left(12-x-y\right)$
Question: It appears the textbook defines 12=x+y or 0=12-x-y as G(f,x). This makes no sense to me as 12-x-y must equal zero. If defined as G(f,x), this means the output could be something other than zero, which it cannot. What am I missing here? Thanks!