Amelia runs a catering business. Based on her records, her

weekly profit can be approximated by P = 2x2 - 44x – 150,

where x is the number of meals she caters and P is her profit.

When P is negative, Amelia has lost money.

1) What is the least number of meals Amelia needs to cater

in order to begin making a profit?

2) If she caters no meals one week, how much money does

she lose?

3) What is her profit for catering 50 meals?

(1) The least number of meals is 26 (2) She loses 150 if she caters no meal in one week. (3) Her profit would be 2,650 if she caters for 50 meals in one week

Step-by-step explanation: The weekly profit is given as a quadratic equation which is;

P = 2x² -44x - 150

We begin by solving for the value of x.

When 2x² -44x - 150 = 0

Divide all through by 2

x² - 22x - 150 = 0

By factorization,

(x - 25) (x + 3) = 0

(x -25) = 0 OR (x + 3) = 0

When x - 25 = 0

x = 25

When x + 3 = 0

x = -3

What this implies is that when Amelia caters for 25 meals in a week, her profit is calculated as follows

P = 2x² - 44x -150

P = 2(25)² - 44(25) - 150

P = 2(625) - 1100 - 150

P = 1250 - 1100 - 150

P = 0

(1) Therefore she must cater for at least 26 meals before she can begin to make any profit.

(2) She loses 150 if she caters no meal in one week.

This can be calculated as follows;

When x = 0,

P = 2x² - 44x - 150

P = 2(0)² - 44(0) - 150

P = 0 - 0 -150

P = -150

(3) When she caters 50 meals her profit becomes 2,650

P = 2x² - 44x - 150

P = 2(50)² - 44(50) - 150

P = 2(2500) - 2200 - 150

P = 5000 - 2200 - 150

P = 2650