A gadget manufacturer has developed a profit model that depends on x number of gadgets per month sold and y hours per month of advertising, according to the function P(x, y) = 9x2 + 36xy − 4y2 − 18x − 18y, where P is measured in thousand dollars. If the budgetary constraint is 3x + 4y = 32, use the method of Lagrange Multipliers to find the maximum profit.

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