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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. S = 2020.30 0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min 50L +100C s.t. 2020.300.70 = 55,000 LCO (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C> 0. Round your answers to the nearest integer.) $ X at (L, C) =