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 60,000 tons of steel at minimum cost.

min	100C+50L
s.t.
	20C0.7L0.3 = 60,000
	L, C 0

(b)

Solve the optimization problem you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5,000 for both L and C before solving. (Round your answers to three decimal places.)

$

at (L, C) =