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 = 20 L0.3 C 0.7 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $40, and each unit of capital costs $120. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. Min 40 L + 120 C 20 L0.3 C 0.7 50000 L, C 0 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial L > 0 and C > 0. If required, round your answers to two decimal places.