The maximum profit occurs where the gradient equals zero, or in other words, where both the partial derivative wrt x and the partial derivative wrt y are zero at the same time.
Knowing this, can you solve this problem?
A company advertises on Radio and TV for its product. the profit based on these advertisement has been
determine in 1000 is as P(x,y)=-2x^2-xy-y^2+8x+9y+10
where x is the amount spent on Radio and y is the amount spend on TV respectively. How much money should
be spent on both advertisement to maximize the profit?