Answer
(a) 72
(b) 72
Work Step by Step
(a) Start by taking the partial derivative of R with respect to x_{1}. When taking the partial derivative, treat x_{2} like a constant and apply the power rule to obtain:
Partial derivative of R with respect to x_{1} = 200 - 8x_{1} - 8x_{2}
Now plug in x_{1} = 4 and x_{2} = 12 to obtain the marginal revenue for plant 1: 200 - 8\times(4) - 8\times(12) = 72
(b) Now take the partial derivative of R with respect to x_{2}.
Partial derivative of R with respect to x_{2} = 200 - 8x_{2} - 8x_{1}
Again plug in x_{1} = 4 and x_{2} = 12 to obtain the marginal revenue for plant 2: 200 - 8\times(12) - 8\times(4) = 72
