Let S represent the amount of steel produced (in tons). Steel production is rela
ID: 3317245 • Letter: L
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 = 10 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 $60, 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_______ L +_______ C __________ L0.4C 0.6 - = ________ L, C >____________ - (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 = $Explanation / Answer
(A)
Min Cost = 60L + 100C
10 L0.4C 0.6 = 40000
L, C 0
(B)
Upper bound constraints
L<=6000
C<= 6000
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