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 = 20L0.30 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 40,000 tons of steel at minimum cost. Min s.t. L, C 20 $ = 40,000 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the neares integer.) at (L, C) =

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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 = 20L0.30 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 40,000 tons of steel at minimum cost.
Min
s.t.
L, C20
$
= 40,000
(b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the nearest
integer.)
at (L, C) =
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 = 20L0.30 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 40,000 tons of steel at minimum cost. Min s.t. L, C20 $ = 40,000 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the nearest integer.) at (L, C) =
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