Problem EF1. The population of magenta-spotted dodecahedral fish in a particular fishery follows the growth function F(x) = 987x - 0.45x if the population is left undisturbed, were x is population. What is the equilibrium natural population? Assume that fractional fish are possible. Problem EF2. For the fishery in Problem EF1, what is the maximum sustained yield, and the corresponding population? Problem EF3. Humans discover the magenta-spotted dodecahedral fish fishery and begin to harvest at a yield of h = 8Ex, where E is the amount of fishing effort and x is population. Find sustainable population x as a function of effort E.Note: You can use this equation solver to solve any single-variable equations after you set them up. The focus of these problems is not on algebraic manipulations, but on the concepts and the procedure involved. Problem KTC1. Use the Kuhn-Tucker conditions to find maximum for the following: F(x, y) = 2x y, subject to constraints (v) 18x + 3y s 1266 and (vi) 2x + 5y s 1000. Assume that x and y must each be greater than or equal to 0. Problem KTC2. Use the Kuhn-Tucker conditions to find maximum for the following: F(x, y) = xy, subject to constraints (vii) x3 + y'