More and more seafood is being farm-raised these days. A model (differential equation) used for the rate of change for a fish population, P(t) in farming ponds is given by P'(t) = b(1-(P(t)/Pm)) - hP(t) where b is the birth rate, PM is the maximum number of fish the pond can support, and h is the rate the fish are harvested. Write a python code that implements the Forward Euler method to solve the differential equation Suppose that the carrying capacity PM = 20, 000 fish with a birth rate of 6% and a harvesting rate of h = 0%, use your Python code to find and plot the numerical solution for the first 400 days for different values of y0. Pick y0 < 20, 000, y0 > 20, 000. Don’t forget to label all your plots with x and y axes label, titles and legends. Use a time step ∆t = 0.1

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Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.