Question

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 L^0.3C ^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 L0.3C 0.7 - Select your answer -≤≥<>=Item 4 L, C - Select your answer -≤≥<>=Item 6
(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 = $

Answer 1

Solution:

(a)

Min Z = 40L + 120C

20L0.3C0.7 >= 50,000

L,C >= 0

(b)

L= 2990.86

C=2318.44

Cost = 397447.6