Your weekly cost (in dollars) to manufacture x cars and y trucks is given by $C ( x , y ) = 270,000 + 6,800 x + 3,000 y - 200,000 e ^ { - 0.03 ( x + y ) }$
What is the marginal cost of a car ? Of a truck ?

A)Marginal cost of a car is $6,800 + 6,000 e ^ { - 0.03 x }$ marginal cost of a truck is $3,000 + 6,000 e ^ { - 0.03 y }$
B) Marginal cost of a car is $6,800 - 200,000 e ^ { - 0.03 ( x + y ) }$
Marginal cost of a truck is $3,000 - 200,000 e ^ { - 0.03 ( x + y ) }$
C) Marginal cost of a car is $3,000 + 200,000 e ^ { 0.03 ( x + y ) }$
Marginal cost of a truck is $6,800 + 200,000 e ^ { 0.03 ( x + y ) }$
D) Marginal cost of a car is $3,000 - 6,000 e ^ { 0.03 ( x + y ) }$
Marginal cost of a truck is $6,800 - 6,000 e ^ { 0.03 \{ x + y \} }$
E) Marginal cost of a car is $6,800 + 6,000 e ^ { - 0.03 ( x + y ) }$
Marginal cost of a truck is $3,000 + 6,000 e ^ { - 0.03 ( x + y ) }$

Question

Your weekly cost (in dollars) to manufacture x cars and y trucks is given by   $C ( x , y ) = 270,000 + 6,800 x + 3,000 y - 200,000 e ^ { - 0.03 ( x + y ) }$  
What is the marginal cost of a car ? Of a truck ?
 
A)Marginal cost of a car is $6,800 + 6,000 e ^ { - 0.03 x }$ marginal cost of a truck is $3,000 + 6,000 e ^ { - 0.03 y }$
B) Marginal cost of a car is $6,800 - 200,000 e ^ { - 0.03 ( x + y ) }$
Marginal cost of a truck is $3,000 - 200,000 e ^ { - 0.03 ( x + y ) }$
C) Marginal cost of a car is $3,000 + 200,000 e ^ { 0.03 ( x + y ) }$
Marginal cost of a truck is $6,800 + 200,000 e ^ { 0.03 ( x + y ) }$
D) Marginal cost of a car is $3,000 - 6,000 e ^ { 0.03 ( x + y ) }$
Marginal cost of a truck is $6,800 - 6,000 e ^ { 0.03 \{ x + y \} }$
E) Marginal cost of a car is $6,800 + 6,000 e ^ { - 0.03 ( x + y ) }$
Marginal cost of a truck is $3,000 + 6,000 e ^ { - 0.03 ( x + y ) }$

Quizplus · Accepted Answer

The marginal cost of a car or a truck is found by taking the partial derivative of the cost function with respect to the variable of interest (x for cars, y for trucks). The correct marginal costs account for the derivative of the exponential term with respect to both x and y, which affects both the cost of cars and trucks equally due to the shared term $-0.03(x+y)$ in the exponent.

Your Weekly Cost (In Dollars) to Manufacture X Cars and Y