Question

The equation p = −5x2 + 100x − 250 models the profit p in dollars from selling pizza, where x is the price per pizza in dollars. What is the highest price you can charge per pizza to profit $100?

Answer 1

Answer:

$23.0384

Step-by-step explanation:

p = −5x2 + 100x − 250

Where,

P = profits in dollars

x = price in dollars

Find x when p = $100

p = −5x2 + 100x − 250

100 = −5x² + 100x − 250

100 + 250 = -5x² + 100x

350 = -5x² + 100x

-5x² + 100x - 350 = 0

x = -b ± √(b² - 4ac) / 2a

= -100 ± √(100² - 4*-5*-350) / 2*-5

= -100 ± √10000 - (-7000) / -10

= -100 ± √ 10000 + 7000 / -10

= -100 ± √ 17,000 / -10

= -100 ± 10√170 / -10

= -100/-10 ± 10√170/-10

x = 10 ± √170

x = 10 + √170 or 10 - √170

x = 23.0384 or -3.0384

Price of pizza can't be negative

Therefore, the highest price you can charge per pizza to profit $100 is $23.0384