Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x ≥ 10.

1.describe the meaning of the number 12 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number -100 in the formula, in terms of its meaning in relation to the profit.
3.find the profit for 5 different values of x
4.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 straight line 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.
5.will this profit function have a maximum, if so, what is it?
6.what steps should the company take to prepare for your answer to part 5?

1. The number 12 in the formula represents the profit made per item sold. This means that for every additional item sold, the profit increases by $12,000.

2. The number -100 in the formula represents the fixed costs or expenses that the company incurs regardless of the number of items sold. It could include costs such as rent, utilities, and salaries. This means that even if no items are sold, the company will still have to bear these costs, resulting in a negative impact on the profit.

3. To find the profit for different values of x, we can simply substitute the given values into the formula, P(x) = 12x - 100. Let's assume the values of x are 10, 15, 20, 25, and 30:

P(10) = 12(10) - 100 = 120 - 100 = $20,000
P(15) = 12(15) - 100 = 180 - 100 = $80,000
P(20) = 12(20) - 100 = 240 - 100 = $140,000
P(25) = 12(25) - 100 = 300 - 100 = $200,000
P(30) = 12(30) - 100 = 360 - 100 = $260,000

4. To graph the profit function, we can plot the values calculated in part 3 on a graph with the x-axis representing the number of items sold and the y-axis representing the profit. The graph will be a straight line connecting these points. Please refer to the attached Word file for the graph.

5. Yes, this profit function will have a maximum point. To find the maximum, we can analyze the slope of the line. Since the coefficient of x is positive (12), the slope of the line is positive as well. This indicates that as the number of items sold increases, the profit also increases. However, there will be a point where the increase in profit will start to slow down until it reaches a maximum. Beyond that point, any further increase in the number of items sold will result in a decrease in profit.

6. To prepare for the maximum profit, the company should focus on identifying the optimal level of production/sales where the profit will be maximized. This could involve conducting market research, analyzing demand and competition, and understanding production capacity. The company should also consider cost management strategies to ensure that the fixed costs do not outweigh the potential profit.

1. The number 12 in the formula represents the profit contribution per item sold. It indicates that for every thousand items sold, the profit increases by $12,000. In other words, each additional item sold contributes $12,000 to the annual profit.

2. The number -100 in the formula represents the fixed costs or the costs incurred even if no items are sold. It includes expenses such as rent, utilities, salaries, etc. This means that regardless of the number of items sold, there will be a cost of $100,000. This value is subtracted from the profit contribution per item to account for these fixed costs.

3. To find the profit for different values of x, substitute the given values of x into the profit function P(x) = 12x - 100.

For example:
- For x = 10 (10,000 items sold):
P(10) = 12(10) - 100
= 120 - 100
= $20,000

- For x = 12 (12,000 items sold):
P(12) = 12(12) - 100
= 144 - 100
= $44,000

- For x = 15 (15,000 items sold):
P(15) = 12(15) - 100
= 180 - 100
= $80,000

- For x = 20 (20,000 items sold):
P(20) = 12(20) - 100
= 240 - 100
= $140,000

- For x = 25 (25,000 items sold):
P(25) = 12(25) - 100
= 300 - 100
= $200,000

4. To graph the profit function, plot the values of x on the x-axis and the corresponding profits on the y-axis. Connect these points with a straight line to generate a linear graph. You can use Excel or any other graphing utility to create the graph.

5. Since the profit function is linear (in the form P(x) = mx + b), it will not have a maximum. The profit will continue to increase as more items are sold, and there is no upper limit or maximum profit value.

6. To prepare for the fact that the profit function does not have a maximum, the company should focus on maximizing sales and minimizing costs. They can explore strategies to increase the number of items sold, such as marketing campaigns, expanding their customer base, optimizing product offerings, etc. Additionally, they should continuously review and optimize their costs to ensure they are as efficient as possible. Regular financial analysis and review will help identify areas for improvement and identify opportunities for growth.