A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table

Amount of Fertilizer (pounds/acre)	250	500	750	1000	1250	1500	1750	2000
Revenue earned (dollars/acre)	96	145	172	185	192	196	198	199

The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following.

• Is each pound of fertilizer equally effective? Explain.
• Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate k.
• Compute a linear regression for the data.
• Compute a logarithmic regression(LnReg) for the data.
• Use trial and error on your calculator to fit a function of the form r=k(1−bx)r=k(1-bx) where k is the estimate for the maximum amount of revenue and 0
• Choose the best model for revenue and then write a total cost function for fertilizer. Use graphs on your calculator to find where cost equals revenue. 
• Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.

Answer rating: 100% (QA)

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