The joint cost (in dollars) for two products is given by , where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find the marginal cost with respect to x if 2 units of product X and 9 units of product Y are produced.
C)
D)
E)

Question

The joint cost (in dollars) for two products is given by  , where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find the marginal cost with respect to x if 2 units of product X and 9 units of product Y are produced. ​
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

To find the marginal cost with respect to x, we need to take the partial derivative of the joint cost function with respect to x.

∂C/∂x = 3x^2 - 18xy + 12y^2

Substituting x = 2 and y = 9, we get:

∂C/∂x = 3(2)^2 - 18(2)(9) + 12(9)^2
        = 12 - 324 + 972
        = 660

Therefore, the marginal cost with respect to x when 2 units of product X and 9 units of product Y are produced is 660, which is equivalent to choice B.

The Joint Cost (In Dollars) for Two Products Is Given