At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by $dP over dx space equals space 100 minus 12 square root of straight x$ . If the firm employs 25 more workers, then
the new level of production of items is

2500

3000

3500

4500

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Solution

3500

dP over dx space equals space 100 minus 12 square root of straight x On space integrating space both space sides comma space we space get integral subscript 2000 superscript straight P dP space equals space integral subscript 0 superscript 25 left parenthesis 100 minus 12 square root of straight x right parenthesis dx left parenthesis straight P minus 2000 right parenthesis space equals space 25 space straight x space 100 minus fraction numerator 12 space straight x space 2 over denominator 3 end fraction space left parenthesis 25 right parenthesis to the power of 3 divided by 2 end exponent straight P space equals space 3500

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