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 L0.30 C 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 50,000 tons of steel at minimum cost.. your answer is zero, enter "0". 50 L Min s.t. 20 20.30 C 0.70 L, C 2 100 c ; 50000
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 L0.30 C 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 50,000 tons of steel at minimum cost.. your answer is zero, enter "0". 50 L Min s.t. 20 20.30 C 0.70 L, C 2 100 c ; 50000
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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:
520 1030 C0.70
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 50,000 tons of steel at minimum cost. If
your answer is zero, enter "0".
Min
s.t.
L
=
C
50
Cost $
20
1914
(b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial L> 0 and C > 0.
Do not round intermediate calculations. Round your answers to the nearest whole number.
3829
0.30 C 0.70
478625
L, C
2
100 c
50000
0
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