# A company has found that when x units of a product are manufactured and sold, its revenue is given by x 2 + 100 x dollars and its costs are given by 240 x + 500 dollars. How many units must be produced and sold to make a profit of 10,000 dollars?

Tushar Chandra | Certified Educator

calendarEducator since 2010

starTop subjects are Math, Science, and Business

The profit made is equal to revenue - costs.

For x number of units the profit is given by x^2 + 100x - 240x - 500.

To make a profit of 10000, let the number of units to be produced be x.

x^2 + 100x - 240x - 500 = 10000

=> x^2 - 140x - 10500 = 0

x = [-b + sqrt (b^2 - 4ac)]/ 2a

=> [ 140 + sqrt (  140^2 + 4*10500)]/ 2

=> [ 140 + sqrt 61600]/ 2

=> 70 + 5*sqrt 616

=> 194.096

As the number of units cannot be fractions it has to make 195 units.

The number of units to make a profit of \$10000 is 195.

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## Related Questions

hala718 | Certified Educator

calendarEducator since 2008

starTop subjects are Math, Science, and Social Sciences

Let the revenue be R, the profit be P, and the cost be C.

Then, we know that:

Profit = Revenue - cost

==> Given that R= x^2+100x

Also, given that C = 240x+500

==> P = x^2 +100x - 240x -500

==> P = x^2 -140x -500

We need to find x such that P= 10,000

==> x^2 - 140x -500 = 10,000

==> x^2 -140x -10,500 = 0

We will use the formula to find the roots.

==> x1= ( 140+248.2)/2 = 194.1 ( approx.)

Then, the number of product must be sold is 194.

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