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 L0.2 C 0.8 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 $120. (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. If your answer is zero, enter "0". Min s.t. L C = Cost = $ 10.2 c 0.8 + L, C C Select your answer Select your answer - ✓ (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. L =
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 L0.2 C 0.8 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 $120. (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. If your answer is zero, enter "0". Min s.t. L C = Cost = $ 10.2 c 0.8 + L, C C Select your answer Select your answer - ✓ (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. L =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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:
S = 15 L0.2 C 0.8
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 $120.
(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. If
your answer is zero, enter "0".
Min
s.t.
L
C =
Cost = $
10.2 c 0.8
+
C
- Select your answer - V
L, C- Select your answer -
(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.
L =
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