The function p(x) = −2000x2 + 18000x − 15000 models the monthly profit P of a smoothie company, where x represents the price per smoothie. Identify the price range that will generate a monthly profit of at least $25,000. a. Between $4 and $5; inclusive b. Less than $4 c. Between $4 and $5; exclusive d. More than $5

Step-by-step explanation:

Givem the profit function

p(x) = −2000x2 + 18000x − 15000

We are to generate the price range that will generate a monthly profit of at least $25,000

Substitute into the function we have;

25000 = −2000x2 + 18000x − 15000

Divide through by 1000

25 = -2x²+18x-15

Rearrange

-2x²+18x-15-25 = 0

2x²-18x+40 = 0

Divide through by 2

x²-9x+20 = 0

Factorize

x²-5x-4x+20 = 0

x(x-5)-4(x-5) = 0

x-4 = 0 and x-5 = 0

x = 4 and x = 5

Hence the price range that will generate a monthly profit of at least $25,000 is between $4 and $5 inclusive