Suppose the daily total cost (in dollars) of manufacturing x televisions is What is the marginal cost when x = 600? What is the actual cost incurred in manufacturing the 601st television?
A)$348.00, $348.58
B)$186.67, $186.94
C)$348.00, $348.46
D)$186.67, $186.98

Question

Suppose the daily total cost (in dollars) of manufacturing x televisions is  What is the marginal cost when x = 600? What is the actual cost incurred in manufacturing the 601st television?
A)$348.00, $348.58 
B)$186.67, $186.94 
C)$348.00, $348.46 
D)$186.67, $186.98

Quizplus · Accepted Answer

To find the marginal cost, we need to take the derivative of the total cost function and evaluate it at x=600.
d/dx(11x^(1/2)+800/x)=11/(2x^(1/2))-800/x^(2)
d/dx(11eaa3e5_55ee_e85a_9f8f_23536d60b581_TB5971_11)=11/(2*600^(1/2))-800/600^(2)=348/300=1.16

Therefore, the marginal cost when x=600 is $348.00 (option C).

To find the actual cost incurred in manufacturing the 601st television, we need to calculate the difference between the total cost of manufacturing 601 televisions and the total cost of manufacturing 600 televisions.
11(601)^(1/2)+800/601-(11(600)^(1/2)+800/600)=348.46-348.00=0.46

Therefore, the actual cost incurred in manufacturing the 601st television is $0.46 (option C).

Suppose the Daily Total Cost (In Dollars) of Manufacturing X