Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ≥ 0.

describe the meaning of the number -.1 in the formula, in terms of its meaning in relation to the profit.
describe the meaning of the number -300 in the formula, in terms of its meaning in relation to the profit.
find the profit for 5 different values of x
graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a smooth curve in Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.

It means profit decreases ultimately.

Look at profit per unit

P(x)/x= -1x+50-300/x

This is a company which is not being run well. Graph it as directed.

The number -.1 in the formula represents the coefficient of the quadratic term (-.1x^2) in the profit function. In terms of its meaning in relation to the profit, it indicates the rate at which the profit decreases as the number of items sold (x) increases. Since the coefficient is negative (-.1), it suggests that the profit curve is concave downwards, meaning that as more items are sold, the profit will decrease at an accelerating rate.

The number -300 in the formula represents the constant term in the profit function. In terms of its meaning in relation to the profit, it indicates the profit value when no items are sold (x = 0). In this case, -300 means that when no items are sold, the company is experiencing a loss of $300, which is subtracted from the profit for any positive value of x.

To find the profit for different values of x, you can substitute those values into the profit function, P(x) = -.1x^2 + 50x - 300, and calculate the result. Let's calculate the profit for 5 different values of x:

1. For x = 0:
P(0) = -.1(0)^2 + 50(0) - 300
= 0 - 0 - 300
= -300
The profit when no items are sold is -$300.

2. For x = 10:
P(10) = -.1(10)^2 + 50(10) - 300
= -.1(100) + 500 - 300
= -10 + 500 - 300
= 190
The profit when 10 items are sold is $190.

3. For x = 20:
P(20) = -.1(20)^2 + 50(20) - 300
= -.1(400) + 1000 - 300
= -40 + 1000 - 300
= 660
The profit when 20 items are sold is $660.

4. For x = 30:
P(30) = -.1(30)^2 + 50(30) - 300
= -.1(900) + 1500 - 300
= -90 + 1500 - 300
= 1110
The profit when 30 items are sold is $1110.

5. For x = 40:
P(40) = -.1(40)^2 + 50(40) - 300
= -.1(1600) + 2000 - 300
= -160 + 2000 - 300
= 1540
The profit when 40 items are sold is $1540.

To graph the profit function, you can use Excel or any other graphing utility. Plot the x-values (number of items sold) on the x-axis and the corresponding profit values on the y-axis. Connect the points with a smooth curve. Using the 5 values calculated above, you can plot these points and then connect them to create the graph. Once done, save the graph to a Word file and attach it in the class DB thread.