The total cost (in thousands of dollars) of a machine manufacturing unit is given by the function T(x) = 300 + 5x, where x is the number of machines produced. What is the average cost (in thousands of dollars) of manufacturing 200 machines? (Average cost is the ratio of total cost to the number of machines manufactured.)
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To find the average cost of manufacturing 200 machines, we need to divide the total cost by the number of machines produced.
The total cost function is given as T(x) = 300 + 5x, where x is the number of machines produced.
Substituting x = 200, we get: T(200) = 300 + 5(200)
T(200) = 300 + 1000
T(200) = 1300
So, the total cost of manufacturing 200 machines is 1300 thousand dollars.
Now, we can calculate the average cost by dividing the total cost by the number of machines produced:
Average cost = Total cost / Number of machines produced
Average cost = 1300 / 200
Average cost = 6.5
Therefore, the average cost of manufacturing 200 machines is 6.5 thousand dollars.
According to the directions
Average cost = (300+5x)/x