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Profit Maximization and Profit Function

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Q2. A firm's profit function is given by:
Profit = 108 + 2X^2 -4 XY + 3Y^2 - 8X - 12Y
Determine:
(a) the values of X and Y that maximize profit.
(b) the maximum value of profit.

I've taken the 1st derivate for X & Y, solves for x and equated these two against each other and and get X = 10. Plug this X value in and I get Y = 12

When I take the second derivate for x & Y, I get positive numbers which means these values are't max. Using these same values (X = 10, Y = 12) plugged into the profit function gives a profit of zero which is strange and obviously not profit maximizing values.

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Profit = 108 + 2x2 - 4xy + 3y2 - 8x - 12y
a) Determine the values of X and Y that maximize profit.
Begin by computing partial derivatives:

= 4x - 4y - 8

= -4x + 6y - 12

Solve for x and y, first by ...

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