S = Problem 8-08 (Algorithmic) Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function: 40-0.60 2.0 In this formula L represents the units of labor input and the units of capital input. Each unit of labor costs $150, and each unit of capital costs $200. a. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 70,000 tons of steel at minimum cost. If the constant is "1" it must be entered in the box: if your answer is zero, enter "0". Min 150 2+ 200 s.t. 0.6 0.4 40 2 C 70,000 LCE b. Solve the optimization problem you formulated in part (a). Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of O and 5000 for both L and C before solving. Round your answers for L and C to three decimal places. Round your answer for optimal solution to one decimal place. L = and C = for an optimal solution of $