Question: A commercial vegetable and fruit grower carefully observes the relationship between the per-acre 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 (pounds/acre) Extra revenue earned (dollars/acre)
0 0
288 250
435 500
516 750
555 1000
576 1250
588 1500
594 1750
597 2000
1. The fertilizer costs 42 cents per pound. What would you advise the grower is the most profitable amount of fertilizer to use?
2. Estimate the maximum amount of extra revenue that can be earned per acre byobserving the data.
3. Graph the data points giving the extra revenue made from improved pumpkin salesas a function of the amount of fertilizer used. What does the graph tell you about thegrowth 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?
5. Determine a function that models the total cost of the fertilizer as a function of the amount of fertilizer used. Graph your fertilizer cost function on the graph you created for Question 4. 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 per acre that can be made and the amount of fertilizer per acre that would result in that maximum extra profit.