Statement: Shelly has a small tomato farm. She can sell the tomatoes for $0.30 per pound. She currently plants 1000 tomato plants on her farm and obtains 30 pounds of tomatoes per plant. The county agricultural agent told her that for each additional plant she adds the number of pounds of tomatoes per plant decreases by 0.02 pound. How many additional plants should she add (or subtract) in order to maximize her revenue? Define the problem: 1. What are the variables (unknowns) in this problem? Give each variable a letter name. 2. What are the constants (numbers) in this problem? 3. How much money (revenue) does she currently make from her tomato farm? How did you find the answer? Devise a plan: 4. Make a table showing the total number of tomato plants on Shelly's farm if she adds O plants, 1 plant and 2 plants. Use x for the additional plants. 5.Convert the table in question 4 to a linear equation with independent variable the number of plants added (x) and dependent variable the total plants. 6. Make a table showing the yield in pounds per plant on Shelly's farm if she adds 0 plants, 1 plant and 2 plants. Use x for the additional plants. 7. Convert the table in question 6 to a linear equation with independent variable the number of plants added (x) and dependent variable the pounds per plant. 8. What function is going to used showing the revenue as a function of the number of tomato plants added ( x) by finding the product of the total plants function, pounds per plant function, and the price per pound Shelly gets for her tomatoes. 9. The revenue function found in 8 is in factored form. What form should you convert this equation to, if you want to use it to find the maximum revenue? Carry out the plan. 10. Convert the equation in 8 from factored form. Find the vertex of this quadratic function. Be sure to include units for both h and k. 11. Make a sentence telling Shelly how many tomato plants to add to the 1000 plants she already has and how much revenue she can expect to make. Look back. 12. a) Did you use a symbolic (algebraic) approach to find the maximum revenue? b) What other approach could you have used to solve this problem in a different way? 13. What did you learn by completing this project that you might use in solving other problems in the future