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 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	L	+	C
	L0.3 C 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