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# 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?

10 years ago

hello ,

this is really an easy but tricky question ...we will start with...

Let us use profit = revenue - costs to find a formula for the profit P

P = ( x 2 + 100 x ) - ( 240 x + 500 )

Substitute P in the above equation by 10,000 dollars to obtain

10000 = x 2 - 140 x - 500

Write the equation in standard form and solve for x

x 2 - 140 x - 10500 = 0

Solve the above equation for x

x = 194.10 and x = -54.01

The number of units to produce must be positive, so

x = 194.

As an exercise, check that for the above value of x the profit is approximately (because of the rounding) equal to 10,000.