A company uses two intermediate products to produce their end product. The profit when using x (in thousands) of product 1, and z (in hundreds) of product 2 is known to be
P = (x − 0.5)(z − 1)(11 − 2x − z) + 500
Both products are limited, we have x ≤ 6 and z ≤ 10.
I am trying to find out which combination of x and z will create the Maximum Profit.
Currently I have determined the first derivative as (z-1)(-4x-z+12)
I am unsure how to progress from here with two variables as well as the limit imposed on both variables. Does anyone know the procedure for this type of Profit Maximization Question?