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?
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Expert Answers
calendarEducator since 2010
write12,551 answers
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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calendarEducator since 2008
write3,662 answers
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.