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Question

A present, a firm is manufacturing 1000 items, It is estimated that the rate of change of production P with respect to the additional number of workers x is given by dpdx=100-12x. If the firm employs 25 more workers, then the new level of production of the item is


A

2500

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B

3000

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C

3500

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D

4500

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Solution

The correct option is A

2500


Explanation for the correct option:

Step 1: Integrate the given function:

Given: dpdx=100-12x

Multiply both sides with dx and integrate both sides.

dp=100-12xdxp=100x-8x32+c

Step 2: Find the value of the constant:

Put x=0 and p=1000 to get the value of C.

1000=100·0-8·032+cc=1000

So, p=100x-8x32+1000

Step 3: Find the new level by putting the value on the increase in workers:

Put x=25 in the obtained equation.

p=100·25-8·2532+1000=2500-1000+1000=2500

Hence, option (A) is the correct answer.


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