The profit is the difference between the revenue and the cost, so we have
Let's compute the partial derivatives:
To find the point of maximum, we have to impose the gradient to be null:
If we sum the two equations, we have
And we deduce from the first equation
So, the maximum profit is achieved by selling 4000 panels of type A and 6000 panels of type B.
If we plug x=4, y=6 in the profit equation, we have