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 = 20L^0.30C^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 45,000 tons of steel at minimum cost. Min Correct: Your answer is correct. s.t. = 45,000 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. Round your answers to the nearest integer.)