5. (22) The Cobb-Douglas production function for gizmos is given by P(L,K) = 4000-6K0.4 where the values of P represent annual production (in gizmos) and L and K repre- sent annual expenditures on labor and capital goods, respectively, in dollars. If an annual budget of $850,000 is available find the amount which should be expended on labor, and the amount which should be expended on capital goods to maximize gizmo production, using the following steps: (a) Write an equation relating L and K if the entire budget is to be spent. (b) Use this equation to solve for K in terms of L. (c) Plug the expression for K into the formula for P to obtain a function of the one variable, L (d) Solve the resulting one-variable max-min problem. (Hint: there is a closed bounded interval L must lie in for this to make economic sense, at both ends of which it is obvious that gizmo production is 0.) Round your answer to the nearest $ per year. (e) Having found the labor expenditure that maximizes gizmo production, plug into the equation expressing K in terms of L to find the corresponding capital expenditure