1. The following table represents data for total cost per item produced for Company A and Company B. One of them represents a linear model, the other a quadratic -- identify which is which, and explain how you determined the result.
| Items | Cost A | Cost B |
|---|---|---|
| 0 | 20 | 20 |
| 1 | 25 | 23 |
| 2 | 30 | 28 |
| 10 | 70 | 140 |
2. Using the data from (1), determine the equation of the line for the one that is linear and the equation of the quadratic for the one that is quadratic.
3. Suppose the profit for a company is given by $P(x) = 50x - 0.2x^2 - 2000$, where P is the profit and x is the number of units produced.
- Sketch the graph, showing the direction of the parabola and approximate location
- At what value of production is the profit a maximum (or minimum)?