On what day should you want your variety to be harvested in order to maximize your profit per tree? In answering this question, you should include the following:
(a) Graphs of the revenue function R(t) and the cost function C(t) per tree on the same axes. Shade the region that indicates profit.
(b) An explicit formula for the profit function P(t), and a graph of P(t).
(c) Use the Matlab solver to find when P'(t)=0. You can find where an equation is zero using Matlab by using the vpasolve command. For example, if you want to find the solutions to x²-x+2=0, you could use the following sequence of commands
>> syms x;
>> solx =vpasolve(x²-4**x+2==0,x)
(The first command defines your variable (you don't have to use x); the second line uses the vpasolve command to find the numerical solutions).
(d) Indicating on your graph the day it appears your maximum profit per tree will occur. Does it occur at t where P'(t)=0 ? State a relationship about derivatives and where a maximum may occur.
