Solve the problem.
-The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by , is found by dividing C(x) by x. Find
A)14
B)10
C)6
D)Does not exist

Question

Solve the problem.
-The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by  , is found by dividing C(x) by x. Find 
A)14 
B)10 
C)6 
D)Does not exist

Quizplus · Accepted Answer

The average cost per tape is given by the expression 11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 = C(x)/x.
Substituting C(x) = 9000 + 9x, we get:
11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 = (9000 + 9x)/x
Simplifying, we get:
11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 = 9000/x + 9
To minimize the average cost per tape, we need to minimize 11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11. This occurs when x is maximized, since 11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 is a decreasing function of x. However, since x cannot be negative, we choose the smallest positive integer value of x, which is x=1. 
Thus, 11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 = (9000 + 9(1))/1 = 9009/1 = 9009.
Dividing by 1000 to get the answer in thousands, we get 11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 = 9.009.
Rounding off to the nearest integer, we get 11ec8a6f_1803_38c2_bfc5_458bad043c87_TB6722_11 = 9.
Therefore, the answer is B) 10.

Solve the Problem. -The Cost of Manufacturing a Particular Videotape Is C(x) =