Question

The effect of applying x milligrams of drug A and y milligrams of drug B is measured by

 f(x, y) = xy - 2x² - y² + 120x + 40y + 25

 

What amounts of each drug should be used to get the biggest effect?

 

Answer 1

The effect of applying x milligrams of drug A and y milligrams of drug B is measured by the function

The first and second order partial derivatives of this function are

The stationary points can be found by solving the below system of equations.

From the above system of equations, we get

Substituting the value of y, we get

Hence, the only stationary point is (40, 40).

For this stationary point,

Hence, the amounts of each drug that should be used to get the biggest effect are