1. Trend Lines Ex. Suppose the number of students at the University of Arizona since 1990 is given by the following table. Fit several trend lines to the data. Use each trend line to predict the number of students in the years 2004 and 2020. Years since 1990Students at UA 024,155 226,872 429,119 633,482 837,004 1040,653

2. Trend Lines Linear: Approx. 46,956 students in 2004 Approx. 73,756 students in 2020

3. Trend Lines Quadratic: Approx. 49,976 students in 2004 Approx. 100,478 students in 2020

4. Trend Lines Exponential: Approx. 50,493 students in 2004 Approx. 117,710 students in 2020

5. Demand, Revenue, Cost, & Profit Ex. Suppose the following data represents the total number of shoes sold in a month at a particular price in dollars. Use a second degree polynomial trend line to find a formula for the Demand function Number of shoesPrice 200$76 350$68 450$59 700$53 900$40 1100$24

6. Demand, Revenue, Cost, & Profit

7. Generating graph of revenue Use “Plotting Points” method Use interval [0, q] where q is the q-intercept from Demand graph

8. Demand, Revenue, Cost, & Profit

9. Optimal quantity to maximize revenue is about 800 units. Maximum Revenue is about $36,000 Price should be about $45

10. Demand, Revenue, Cost, & Profit Ex. If the fixed cost is $2000 and the variable cost is $35 per unit, determine a formula for total cost and graph C(q). C(q) = 2000 + 35q

11. Demand, Revenue, Cost, & Profit

12. Graph of Revenue and Cost (determine profit)

13. Demand, Revenue, Cost, & Profit Profit function: P(q) = R(q) - C(q)

14. Demand, Revenue, Cost, & Profit Project (Demand)

15. Demand, Revenue, Cost, & Profit Project - Keep units straight - Prices (dollars) - Revenue (millions of dollars) - Quantities in test markets (whole units) - Quantities in national market (thousands of units)

16. Demand, Revenue, Cost, & Profit Project (Demand) - Convert test market data to national data - Determine quadratic demand trend line (8 decimal places)

17. Demand, Revenue, Cost, & Profit Project (Revenue) - Units should be millions of dollars - Typically - Must adjust for units

18. Demand, Revenue, Cost, & Profit Project (Revenue) Must convert revenue to millions of dollars ***Use this formula

19. Demand, Revenue, Cost, & Profit Project (Revenue)

20. Demand, Revenue, Cost, & Profit Project (Cost) - Use COST function from Visual Basic Editor (will be explained in class)

21. Demand, Revenue, Cost, & Profit Project (Cost) 7 parameters for COST function quantity fixed cost batch size 1 batch size 2 marginal cost 1 marginal cost 2 marginal cost 3

22. Demand, Revenue, Cost, & Profit Project (Revenue and Cost) - Graph both R(q) and C(q) - Use “plotting points” method

23. Demand, Revenue, Cost, & Profit Project (Revenue and Cost)

24. Demand, Revenue, Cost, & Profit Project (Profit)

25. Demand, Revenue, Cost, & Profit Project (Revenue and Cost) - Determine important information from graphs Break-even pts at about 300,000 and 800,000 units (zero profit) Max profit at about 575,000 units Negative profit: q 800K Break-even pts Largest gap = max profit

26. Demand, Revenue, Cost, & Profit Project (Revenue and Cost) - Determine important information from graphs Break-even pts at about 300,000 and 800,000 units (zero profit) Max profit at about 575,000 units Negative profit: q 800K Break-even pts Max profit

27. Demand, Revenue, Cost, & Profit Project (What to do) - Create Demand graph using trend lines - Create Revenue and Cost graph - Create Profit graph