Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 29.1, Problem 5E
Program Plan Intro
To determinethe slack form of given linear program.
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How:- Draw the following functions according to the
given Period.
1 X= e-x
0≤x≤10
2 Y = log (x)
oil ≤x≤10
3 y = log 10 (x) ; 1
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 = 35L0.40 0.60
In this formula L represents the units of labor Input and C the units of capital input. Each unit of labor costs $150, and each unit of capital costs $200.
a. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost. If the constant is "1" it must be entered in the box; if your answer is zero, enter "0".
Min
s.t.
L
C
L, C
b. Solve the optimization problem you formulated in part (a). Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5000 for both L and C before solving. Round your answers for L and C to three decimal places. Round your answer for optimal solution to one decimal place.
L=
and C=
for an optimal solution of $.
Please do…
Suppose that the total cost (in dollars) for a product is given by
C(x) = 1200 + 200 In(2x + 1)
where x is the number of units produced.
(a) Find the marginal cost MC function.
MC =
(b) Find the marginal cost when 200 units are produced. (Round your answer to the nearest cent.)
Interpret your result.
O The profit from the next unit will be approximately this amount.
This is the total profit from producing 200 units.
It will cost approximately this amount to make the next unit.
O This is the total cost of producing 200 units.
(c) Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function?
O MC S0
O MC > 0
MC < 0
MC 2 0
MC = 0
%3D
Does it apply in this problem?
O Yes
No
Chapter 29 Solutions
Introduction to Algorithms
Ch. 29.1 - Prob. 1ECh. 29.1 - Prob. 2ECh. 29.1 - Prob. 3ECh. 29.1 - Prob. 4ECh. 29.1 - Prob. 5ECh. 29.1 - Prob. 6ECh. 29.1 - Prob. 7ECh. 29.1 - Prob. 8ECh. 29.1 - Prob. 9ECh. 29.2 - Prob. 1E
Ch. 29.2 - Prob. 2ECh. 29.2 - Prob. 3ECh. 29.2 - Prob. 4ECh. 29.2 - Prob. 5ECh. 29.2 - Prob. 6ECh. 29.2 - Prob. 7ECh. 29.3 - Prob. 1ECh. 29.3 - Prob. 2ECh. 29.3 - Prob. 3ECh. 29.3 - Prob. 4ECh. 29.3 - Prob. 5ECh. 29.3 - Prob. 6ECh. 29.3 - Prob. 7ECh. 29.3 - Prob. 8ECh. 29.4 - Prob. 1ECh. 29.4 - Prob. 2ECh. 29.4 - Prob. 3ECh. 29.4 - Prob. 4ECh. 29.4 - Prob. 5ECh. 29.4 - Prob. 6ECh. 29.5 - Prob. 1ECh. 29.5 - Prob. 2ECh. 29.5 - Prob. 3ECh. 29.5 - Prob. 4ECh. 29.5 - Prob. 5ECh. 29.5 - Prob. 6ECh. 29.5 - Prob. 7ECh. 29.5 - Prob. 8ECh. 29.5 - Prob. 9ECh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5P
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