The total cost of producing and marketing x number of units of a certain product is given by . For what number x is the total cost a minimum? Round answer to nearest unit.

Question

The total cost of producing and marketing x number of units of a certain product is given by  . For what number x is the total cost a minimum? Round answer to nearest unit.

Quizplus · Accepted Answer

To find the value of x that minimizes the total cost, we need to take the derivative of the cost function and set it equal to zero. The derivative of 11eaa948_cd49_d9c6_84bc_73b25c7d8d22_TB2342_11 is 22x - 2400. Setting this equal to zero gives x = 109.1, which rounds to 109. Therefore, the total cost is minimized when x = 109. 
Plugging this value into the cost function gives a total cost of approximately 11eaa948_cd4a_00d9_84bc_fd99a10bcb57_TB2342_11. Therefore, the closest choice is C.

The Total Cost of Producing and Marketing X Number of Units