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? (HINT: profit = revenue - costs)  Choose one.
A) 192  B) 193  C) 194.  D) 195  E) 196
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.   Answer 194.
<result>C</result>
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? (HINT: profit = revenue - costs)