T/F Conceptual Questions and Explanations (2 pts for a true statement, 4 pts for a false statement).

Instructions:

1. A statement is true if it is true in all cases and under all conditions. Otherwise, it is false.
2. If a statement is true, no explanation is needed.
3. If a statement is false, you need to point out the mistakes and come up with a correct statement

______ By definition, reduced costs of all decision variables in a linear program should be non-negative (zero or positive).

Explanations:

______ By definition, dual prices of all constraints in a linear program should be non-negative (zero or positive).

Explanations:

______ If the reduced cost of a decision variable (product) is 5, it means that the value of this decision variable should be zero. In order for this decision variable to be positive (attractive), its objective coefficient needs to be reduced by 5.

Explanations:

______ As long as the right-hand sides (RHS) of all constraints vary within their respective ranges, all dual prices will not change.

Explanations:

______ For a resource (≤) constraint and a (profit) maximization problem, as the right-hand side (RHS) increases, the corresponding dual price will stay the same or decrease. As a result, the objective function (profit) will either stay the same or decrease.

Explanations:

______ If the 100% rule is satisfied, then the optimal solution will not change.

Explanations:

A Cartesian vector can be thought of as representing magnitudes along the x-, y-, and z-axes multiplied by a unit vector (i, j, k). For such cases, the dot product of two of these fectors {a} and {b} corresponds to the product of their magnitudes and the cosine of the angle between their tails as in {a}⋅ {b} = abcos(theta)

The cross product yields another vector, {c} = {a} × {b} , which is perpendicular to the plane defined by {a} and {b} such that its direction is specified by the right-hand rule. Develop and M-file function that is passed two such vectors and returns Theta, {c} and the magnitude of {c}, and generates a three-dimensional plot of the three vectors {a}, {b}, and {c} with their origins at zero. Use dashed lines for {a} and {b} and a solid line for {c}. Test your function using the following cases:

A. a = [ 6 4 2 ]; b = [ 2 6 4 ];

B. a = [ 3 2 -6 ]; b = [ 4 -3 1];

C. a = [ 2 -2 1 ]; b = [ 4 2 -4 ];

D. a = [ -1 0 0 ]; b = [ 0 -1 0 ];

I know how to find theta, {c}, and the magnitude of {c}, I just don't know how to plot a 3-dimensional graph so if someone could help me with that part of the code for MATLAB

1. solve the initial value problem.

(t^(2)+1)y'+2ty=tant , y(0)=2

2.find the solution to this initial value problem.

yy'=e^x+x , y(0)=y_0

y_0 is a nonzero constant.

EXPLAIN ANS PLEASE:

PYTHON

1. s = 'abc'
print(s[0:] + s[-2:2] + s[:1])

2. def mirrorOnWheels(s):
prev = 0
for current in range(1, len(s) - 1):
prev = current - 1
next = current + 1
if s[prev] == s[next]:
break
else:
continue
return 0
return prev
s = 'Good decision!'
print(mirrorOnWheels(s))

3. mixture = {1:[1, 2, 0], 2:[2, 0, 1], 0:[0, 1, 2]}

print(mixture[2][2])

4. noOddHeroes = []
heroes = ['superman', 'batman', 'aquaman']
for hero in heroes:
if len(hero) % 2 == 0:
noOddHeroes.append(hero)
print(noOddHeroes)

5. candyOnStick = 'lolli lolli lolli lollipop lollipop'
wordList = candyOnStick.split('i')
d = {}
for word in wordList:
if word not in d:
d[word] = 1
else:
d[word] += 1
print(len(d))

6. def oldMcDonald(farm):
result = 0
for animal in farm:
if animal[0] in farm[animal]:
result += 1
return result
farm = {'cow':'moo', 'duck':'quack', 'cricket':'chirp'}
print(oldMcDonald(farm))

7. def analyzer(fileName):
inputFile = open(fileName)
line = inputFile.readline()
inputFile.close()
return line.count(',')
quotes = open('alice.txt', 'w')
quotes.write('Now, here, you see, it takes all the running\n')
quotes.write('you can do, to keep in the same place.\n')
quotes.close()
print(analyzer('alice.txt'))

1
Assume that a project has a starting cost of $300,000 in year 1. $40,000 each year in Year 2, 3, and 4. Estimated benefits of the project are $0 in Year 1 and $ 120,000 each year in Year 2, 3, and 4. Use a discount rate of 7% and round the discount rate into two decimal points.

Calculate the NPV for this project.
calculate the project ROI.

(1 point) A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.13, the probability that a roll comes up 1 or 2 is 0.48, and the probability that a roll comes up 2 or 3 is 0.47 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)

A sample of 20 Ohio University students were randomly selected and asked, “How many phone calls did you receive last night?” The numbers below are their responses.

1  2  0  2  4  2  3  4  5  3 0  4  5  6  3  10  7  6  7  11

Compute the IQR of the distribution.

Answers:

a. 6

b. 3

c. 4

d. 2

In this question, you should complete the C program, perfect.c, by implementing the function isPerfect. Open the file perfect.c, complete, compile and run it. When you are sure it is correct, include the c file in your final submission.

* Note: You should first carefuly read the COMMENTS provided for the function isPerfect, and then start completing the function.

* Note: You MUST NOT alter the main function and the prototype/header of the isPerfect function. ONLY develop the body of the function isPerfect.

A perfect number:
An integer number is said to be a perfect number if its factors, including 1 (but not the

number itself), sum to the number.
Examples:
6 is a perfect number because its factors, except itself, are 3, 2, and 1, and 6 = 3+2+1.

12 is not a perfect number because its factors, except itself, are 6, 4, 3, 2, and 1, but 12 ≠ 6+4+3+2+1.

The code:

#include <stdio.h>

/*
* An integer number is said to be a perfect number if its factors, including 1 (but not the number itself), sum to the number.
* For example, 6 is a perfect number because its factors, except itself, are 3, 2, and 1, and 6 = 3+2+1, but 12 is not a perfect
* number because its factors, except itself, are 6, 4, 3, 2, and 1, but 12 ≠ 6+4+3+2+1.
* This function determines whether its integer parameter, num, is a perfect number or not by returning 1 if the number is a perfect number,
* and 0 otherwise.
*/
int isPerfect(int num);

int main(void) {

   for (int i=1; i<=1000;i++) {

       if (isPerfect(i))

           printf("%d is perfect.\n", i);
   }

}

int isPerfect(int num) {

   // Complete the code of the function

}

12a Find an equation of the tangent plane to the surface ? = 2? 2 + ? 2 − 5?, ?? (1, 2, −4).

12b If ? = ? 2 − ?? + 3? 2 and (?, ?) changes from (3, −1) to (2.96, −0.95), compare ∆? and ??.

Calculus 3 question. Please help.

1) An industry representative claims that 50 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners.

a) The probability that none of the dish owners in the sample subscribes to at least one premium movie channel.

The correct answer is = P(X = 0) = 0.0625. But (4! 0!) is that not 6?

I went 4 X 3 X 2 X 1 / 4 X 0 X 0 X 0 = 24/4 = 6? Some one help please!

b) The probability that more than 2 dish owners in the sample subscribe to at least one premium movie channel.

The answer is 1 - [ 0.0625 + P(X=1) + P(X=2)] = 0.3125

I keep getting 0.0625. I went 1-[0.0625 + 0.5 + 0.375. Since P(X=1) = (8)(0.5)(0.125) = 0.5 and P(X=2) = (6(0.25)(0.25) = 0.375  Am i doing factorials wrong?