A commercial vegetable and fruit grower carefully observe 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 (Longer) 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<b<10<b<1 < li=”” style=”box-sizing: border-box;”></b<10<b<1 <>
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.