Answer :
The marginal profit f'(7, -4) is equal to 134. Hence option B is true.
To find the marginal profit, calculate the partial derivative of the profit function f(x, y) with respect to x, and then substitute the given values.
Taking the partial derivative of f(x, y) with respect to x:
f(x,y) = 7x² - 9xy
∂f(x, y)/∂x = 14x - 9y
Now, substituting the given values x = 7 and y = -4 into the derivative:
∂f(7, -4)/∂x = 14(7) - 9(-4)
= 98 + 36
= 134
Therefore, the marginal profit f'(7, -4) is equal to 134.
The correct answer is B. 134.
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