196 II. Agricultural Business Management A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the extra revenue made from the sales of the resulting pumpkin crop. These observations are recorded in the following table. Amount of fertilizer 0 250 500 750 1000 1250 1500 1750 2000 (pounds/acre) Extra revenue earned 096 145 172 185 192 198 199 (dollars/acre) The fertilizer costs 14 per pound. What would you advise the grower is the most prof- itable amount of fertilizer to use? Check your advice by answering the following questions. 1. Is cach pound of fertilizer equally effective? 2. Estimate the maximum amount of extra revenue that can be earned per acre by observing the data. 3. Graph the data points giving the extra revenue made from improved pumpkin sales as a function of the amount of fertilizer used. What does the graph tell you about the growth of the extra revenue as a function of the amount of fertilizer used? 4. Which of the following equations best models the graph you obtained in Question 3? A (a) N = Ca" (b) y = () y = c(1 - -*) 1 + cena Determine a specific equation that fits the observed data. That is, find the value of the constants in the model you have chosen. 5. Graph the total cost of the fertilizer as a function of the amount of fertilizer used on the graph you created for Question 3. Determine an equation that models this relationship. For what amount of fertilizer is the extra revenue earned from pumpkin sales offset by the cost of the fertilizer? 6. Use the graphs or the equations you have created to estimate the maximum extra profit that can be made and the amount of fertilizer per acre that would result in that extra profit