please solve all the question

Problem Statement. A zoo biologist will place three species of amphibians (a toad, a salaman- der, and a caecilian) in an aquarium where they will feed on three different small preys: worms, crickets, and flies. Each day 1,500 worms, 3,000 crickets, and 5,000 flies will be placed in the aquarium. Each amphibian consumes a certain number of preys per day. Table 1 summarizes the relevant data. The biologist wants to know the maximum number of amphibians that can coexist in the aquarium assuming that no more than 1,000 of each species of the amphibians will be placed in the aquarium. Table 1: Maximum Number of Preys Consumed by Each Species of Amphibian. Food Toad Salamander Caecilian Available Worms 2 1 1 1500 Crickets 1 3 2 3000 Flies 1 2 3 5000 1) Formulate the problem as an optimization problem. II) Investigate the existence of solutions of the feasible region using Farkas's Theorem, if possible. III) Investigate the existence of optimal solutions for the optimization problem using Weier- strass's Theorem. IV) Define the closure set of the feasible region. Is it convex? Explain. V) Let S denote the feasible region. a) Can we always separate S and y by a hyperplane, for any y&S? Explain. b) Is there exist a strongly separating hyperplane for S and y, for any y&S? Explain. c) Is there exist a vector p such that p'y > sup{px : x ES}? Explain. VI) Investigate whether the optimization problem is a convex problem or not. VII) Reformulate the problem as a minimization problem if the original problem formulation was a maximization problem (or vice versa)