(Solved): Example 2.1. Let's begin with the following problem: A pig weighing 200 pounds gains 5 pounds per ...

Example 2.1. Let's begin with the following problem: A pig weighing 200 pounds gains 5 pounds per day and costs 45 cents a day to keep. The market price for pigs is 65 cents per pound, but is falling 1 cent per day. When should the pig be sold? Answer: The pig should be sold after eight days, resulting in a maximum profit of $$\$133.20$$. Question 3. Go back to the growing pig problem from lecture (Example $$2.1$$ in notes). Let us augment the problem by now assuming that the weight of the pig after $$t$$ days is given by the formula $$w(t)=\frac{800}{1+3{\mathrm{e}}^{?t/30}}\mathrm{lbs}.$$ Find the optimal time to sell the pig under this new assumption. Use Newton's method to approximate the solution. Justify your initial guess and if it is close enough you shouldn't have to do more than a couple iterations of Newton's method to convince yourself that you've converged to the solution.