Question

In: Statistics and Probability

Let S represent the amount of steel produced (in tons). Steel production is related to the...

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 = 15 L0.4C 0.6

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 $100.

(a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost.
Min L + C
L0.4C 0.6 - 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 = $

Solutions

Expert Solution

(a) Min Z = 40L + 120C

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

L,C >= 0

(b) L= 2990.86

    C=2318.44

   Cost = 397447.6


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