To complete the analysis, Chuck wants to know more about the revenue that he can generate from his farm.
The price of corn, p(y), depends on how much Chuck produces. The price function is speci�ed as
p(y) = 3 0:05y
c. The revenue that Chuck can generate depends on both the price and the quantity of corn produced.
Thus, the revenue function R(y) is
R(y) = p(y)*y = 3y-0.05ysquared
Draw a graph to show the relationship between the revenue and the quantity of corn produced, with
R(y) on the y-axis and y on the x-axis. Label your graph.
To draw the graph of the revenue function R(y) = 3y - 0.05y^2, you can follow these steps:
Step 1: Determine the range of values for y (quantity of corn produced) that you wish to represent on the graph. Let's say you want to consider values of y from 0 to 100.
Step 2: Create a table of values by substituting different values of y into the revenue function. For example, you can choose y = 0, 20, 40, 60, 80, and 100. Calculate the corresponding values of R(y) using the revenue function.
y | R(y)
----------------
0 | 0
20 | 580
40 | 960
60 | 1320
80 | 1560
100 | 1660
Step 3: Plot the points from the table on a graph with the y-axis representing R(y) and the x-axis representing y. Label the axes accordingly.
Step 4: Connect the plotted points with a smooth curve to represent the relationship between the revenue (R) and the quantity of corn produced (y).
Step 5: Label the graph with a title such as "Revenue vs Quantity of Corn Produced" and label the axes with "y" and "R(y)" respectively.
The resulting graph should show an upward-sloping curve that initially rises steeply but then starts to flatten out as the quantity of corn produced increases.