OPERATIONS RESEARCH >INTERNATIONAL EDITI
4th Edition
ISBN: 9780534423629
Author: WINSTON
Publisher: CENGAGE L
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Chapter 5.2, Problem 2P
a.
Explanation of Solution
Optimum solution
- In this case the reduced cost for
- The allowable increase for
- Hence the basic variables remains the same
b.
Explanation of Solution
Shadow price
- The Relevant Shadow Price is ‑$20.
- If demand is decreased by up to 3 cars then the current basis remains optimal.
- So Dual Price may be used to compute new z‑value.
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1. Using one of the method described in class and/or textbook (Section 9.1) convert the following
regular expression into a state transition diagram:
(0+ 10*1)* (01 + 10)
Indicate in your answer how did you arrive at the result as follows: Write down all the state
transition diagrams that you constructed for all the subexpressions and clearly indicate which
diagram corresponds to which expression. Do not simplify any state transition diagram.
2. Consider the following state transition diagram over Σ = {a,b}:
b
A
a
a
C
b
B
a
a
b
D
За
a
Using the method described in class and in the textbook (Section 9.2) convert the diagram
into an equivalent regular expression. Include all the intermediate steps in your answer.
3. Are the languages L1, L2, and L3 below over the alphabet Σ = {a, b, c} regular or non-regular?
Justify your answer carefully.
(a) L₁ = {a¹b2jc²i : i ≥ 0, j > 2}
(b) L₂ = L₁n {akbm c³p: k,m,p≥ 0}
(c) L3 = {a²ib²j+1 : i,j ≥ 0}^{akbm c³p : k,m,p ≥ 0}
(1 point)
By dragging statements from the left column to the right column below, give a proof by induction of the following statement:
an
=
= 9" - 1 is a solution to the recurrence relation an = 9an-18 with ao
=
: 0.
The correct proof will use 8 of the statements below.
Statements to choose from:
Note that a₁ =
9a0 + 8.
Now assume that P(n) is true for all n ≥ 0.
Your Proof: Put chosen statements in order in this
column and press the Submit Answers button.
Let P(n) be the predicate, "a = 9″ – 1".
απ = 90 − 1 =
Note that
Let P(n) be the predicate, "an
9" - 1 is a
solution to the recurrence relation an = 9an-1 +8
with ao = 0."
-
Now assume that P(k + 1) is true.
Thus P(k) is true for all k.
Thus P(k+1) is true.
Then ak+1
=
9ak +8, so P(k + 1) is true.
= 1 − 1 = 0, as required.
Then = 9k — 1.
ak
Now assume that P(k) is true for an arbitrary
integer k ≥ 1.
By the recurrence relation, we have
ak+1 =
ak+1 =
= 9ak + 8 = 9(9k − 1) + 8
This simplifies to
9k+19+8 = 9k+1 − 1
Then 9k+1 − 1 = 9(9*…
Given the following request to an AI chatbot, which response is more accurate? (You should use Google to verify that the factual claims in each response are accurate.)
Prompt
Is this true? The first recorded use of the phrase "when pigs fly" in print is in a 1616 play by Ben Jonson called "The Devil is an Ass," in which a character says, "When pigs fly, good-night!!"
Response
Response A
Response B
Yes, that's true! The phrase "when pigs fly" indeed appears in Ben Jonson's 1616 play The Devil is an Ass and was said during the second act in a conversation between Fitzdottrel and Pug. The phrase was first used to express skepticism or disbelief, suggesting that something is as unlikely to happen as the fanciful idea of pigs flying. This usage is often cited as one of the earliest instances of the phrase in print.
The claim that the phrase "when pigs fly" was first recorded in Ben Jonson's 1616 play "The Devil is an Ass" is not accurate. There is no evidence from the…
Chapter 5 Solutions
OPERATIONS RESEARCH >INTERNATIONAL EDITI
Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5P
Ch. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 11PCh. 5 - Prob. 1RPCh. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - Prob. 4RPCh. 5 - Prob. 6RPCh. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - Prob. 10RPCh. 5 - Prob. 11RPCh. 5 - Prob. 12RPCh. 5 - Prob. 13RPCh. 5 - Prob. 14RPCh. 5 - Prob. 15RPCh. 5 - Prob. 16RP
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