Question

the cost of manufacturing a computer part is related to the quantity produced, x, during a production run. When 100 parts are produced, the the cost is $300. when 600 parts are produced, the cost is $4800. Find an equation of the line relating quantity produced to cost . Write the final answer in the form C= mx+b

Answer 1

Answer:

C = 9x -600

Step-by-step explanation:

When the number of parts produced goes up by 500 from 100 to 600, the cost goes up $4500 from 300 to 4800. Thus the average cost of producing a part is $4500/500 = $9.

If that were the total cost of producing a part, then the first 100 parts would cost $9×100 = $900. They only cost $300, so $600 must be subtracted from the value 9x to get the cost.

... C = 9x -600

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Check

100 parts cost 9·100 -600 = 300 . . . agrees with problem statement

600 parts cost 9·600 -600 = 4800 . . . agrees with problem statement

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Comment on the problem statement

The initial statement tells you "cost ... related to the quantity produced." The question then asks you to "find an equation ... relating quantity produced to cost." The latter statement suggests you want the independent variable to be cost, not quantity. Here, we have made quantity be the independent variable, as suggested by the use of C= in the answer form.