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 $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 50,000 tons of steel at minimum cost.

Min ____L + _____C

_____L^0.3 C^0.7

L, C

(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.

L = $

C = $

Cost = $