Let's make the pig problem (Example 2.1.) from lecture more complex with a new assumption: The rate of change of the market price for pigs is proportional to the current price, i.e., dp/dt=cp for some constant c. Produce a new model, solution, and answer to the problem with this new assumption. Use Newton's Method to find the optimal time to sell the pig accurate to 4 decimal places. Justify your initial guess using a plot of the profit function