The Profit Problem

Name _____________________________

Suppose that fixed costs for a company are $300 per month. In addition the average cost of production per item per month is given by 150 x dollars for x items produced and sold. The company reasons that the more items that are sold, the more they are willing to risk charging more. So the price per items is x² + 7200 dollars. The maximum number of items that can be produced per month due to space constraints is 80

1. What is the monthly cost for producing x items?

2. What is the total cost per month?

3. What is the revenue per month for selling x items?

4. What is the profit per month for producing and selling x items?

5. Over what intervals is the profit increasing?

6. Over what intervals is the profit decreasing?

7. Over what intervals is the profit increasing at an increasing rate?

8. Over what intervals is the profit increasing at a decreasing rate?

9. Over what intervals is the profit decreasing at an increasing rate?

10. Over what intervals is the profit decreasing at a decreasing rate?

11. How many items should be produced to maximize the profit?

12. What is the maximum profit?

13. Is there an interval over which the company is not making a profit? If so approximate it.