Formulate the following problem using the following steps.
a. Define the decision variables.
b. Specify the objective function.
c. Specify the constraints and simplify them so that the left hand side of each constraint only contains terms involving the decision variables.
ChemLabs uses raw materials I and II to produce two domestic cleaning solutions A and B. The daily availabilities of raw materials I and II are 150 and 145 units respectively. One unit of solution A consumes .5 unit of raw material I and .6 unit of raw material II. One unit of solution uses .5 unit of raw material I and .4 unit of raw material II. The profits per unit of solutions A and B are $8 and $10 respectively. The daily demand for solution A lies between 30 and 150 units, and that for solution B between 40 and 200 units. Formulate and solve graphically the optimal daily production amounts of A and B
In: Advanced Math
1. (14) List the elements for each of the following sets:
(1) P({a, b, c}) (Note: P refers to power set)
(2) P{a, b}) - P({a, c})
(3) P(Æ)
(4) {x Î ℕ: (x £ 7 Ù x ³ 7} (Note: ℕ is the set of nonnegative integers)
(5) {x Î ℕ: $y Î ℕ (y < 10 Ù (y + 2 = x))}
(6) {x Î ℕ: $y Î ℕ ($z Î ℕ ((x = y + z) Ù (y < 5) Ù (z < 4)))}
(7) {a, b, c} x {c, d} (Note: x refers to Cartesian product)
2. (12) True or False.
Let R = {(1, 2), (2, 3), (1, 1), (2, 2), (3, 3), (1, 3)}.
(1) R is reflexive.
(2) R is transitive.
(3) R is symmetric.
(4) R is antisymmetric.
3. (16) True or False.
(1) Subset-of is a partial order defined on the set of all sets.
(2) Subset-of is a total order defined on the set of all sets.
(3) Proper-subset-of is a partial order defined on the set of all sets.
(4) Proper-subset-of is a total order defined on the set of all sets.
(5) Less than or equal (<=) is a partial order defined on the set of real numbers.
(6) Less than or equal (<=) is a total order defined on the set of real numbers.
(7) Less than (<) is a partial order defined on the set of real numbers.
(8) Less than (<) is a total order defined on the set of real numbers.
4. (12) True or False.
(1) f (x) = 2x is onto where f: R -> R. (Note: R is the set of real numbers)
(2) f (x) = 2x is one-to-one where f: R -> R.
(3) f(x) = x² is onto where f: R -> R.
(4) f(x) = x² is one-to-one where f: R -> R.
(5) f(x) = x² is onto where f: R -> [0, ∞).
(6) f(x) = x² is one-to-one where f: R -> [0, ∞).
5. (6) Let ℕ be the set of nonnegative integers. For each of the following sentences in first-order logic, state whether the sentence is valid, is satisfiable (but not valid), or is unsatisfiable.
(1) "x Î ℕ ($y Î ℕ (y < x)).
(2) "x Î ℕ ($y Î ℕ (y > x)).
(3) "x Î ℕ ($y Î ℕ f(x) = y).
6. (20) Are the following sets closed under the given operations? Answer yes or no. If the answer is no, please specify what the closure is.
(1) The negative integers under subtraction.
(2) The odd integers under the operation of mod 3.
(3) The positive integers under exponentiation.
(4) The finite sets under Cartesian product.
(5) The rational numbers under addition.
7. (20) True or False. If the answer is true, provide an example (Hint: use subsets of integers and real numbers) as a proof.
(1) The intersection of two countably infinite sets can be finite.
(2) The intersection of two countably infinite sets can be countably infinite.
(3) The intersection of two uncountable sets can be finite.
(4) The intersection of two uncountable sets can be countably infinite.
(5) The intersection of two uncountable sets can be uncountable.
In: Advanced Math
1.
In order to test the claim that average amount spent for lunch per day by MSU students is not $ 7.25. A random sample of 40 students is taken. After calculating sample mean and standard deviation p- value is found to be 0.0482. Which one of the following statement is correct.
Question 6 options:
|
Reject H0 at 95% confidence level |
|
|
Reject H0 at 99% confidence level |
|
|
Reject H0 at 98% confidence level |
|
|
Reject H0 at 96% confidence level |
2. US department of labor wanted to compare the average unemployment rate in two different states California and Washington. From California they took a sample of size 12 and found that sample mean 20.32 and sample standard deviation is 3.55. From Washington they took a sample of size 15 and found that sample mean 21.24 and sample standard deviation is 2.70. Find the critical value (use t-table) to compute 95% confidence interval of the true difference in population.
3.
Following data shows number of ICU admission (X) and number of death per day (Y) for seven days due to COVID-19 virus. Calculate the test value to test the hypothesis there is no significant correlation between X and Y.
|
Day |
ICU admission (X) |
Death (Y) |
|
1 |
21 |
2 |
|
2 |
15 |
5 |
|
3 |
26 |
6 |
|
4 |
30 |
12 |
|
5 |
35 |
15 |
|
6 |
25 |
9 |
|
7 |
40 |
18 |
|
Total |
192 |
67 |
4. According to the data published by Minnesota Dept of Health, as of May 2, 2020 there are total 6228 conformed positive cases of COVID-19 and 395 death due to the virus. Find the point estimate of the death rate due to COVID-19 in Minnesota.
5. The CEO of a large electric utility claims that more than 82 percent of his 2,500,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 200 customers, using simple random sampling. Among the sampled customers, 174 say they are very satisfied. Find the p value to test this claim.
In: Statistics and Probability
Orange Company dividends will grow at 8% during the next 4 years, 7% during year 5, after that they will grow at a 6%. Last year dividend was $1.50. The risk-free rate of return is 4% and the risk premium is 5% What is the value of the stock? Please show calculations
In: Finance
Host A and B are communicating over a TCP connection, and Host B has already received from A all bytes up through byte 99. Suppose Host A then sends two segments to Host B back-to-back. The first and second segments contain 30 and 70 bytes of data, respectively. In the first segment, the sequence number is 100, the source port number is 4321, and the destination port number is 80. Host B sends an ACK whenever it receives a segment from Host A, i.e., no delayed ACK.
In: Computer Science
For Java
"Simon Says" is a memory game where "Simon" outputs a sequence of 10 characters (R, G, B, Y) and the user must repeat the sequence. Create a for loop that compares the two strings starting from index 0. For each match, add one point to userScore. Upon a mismatch, exit the loop using a break statement. Ex: The following patterns yield a userScore of 4: simonPattern: R, R, G, B, R, Y, Y, B, G, Y
import java.util.Scanner;
public class SimonSays {
public static void main (String [] args) {
String simonPattern = "";
String userPattern = "";
int userScore = 0;
int i = 0;
userScore = 0;
simonPattern = "RRGBRYYBGY";
userPattern = "RRGBBRYBGY";
System.out.println("userScore: " +
userScore);
return;
}
}
In: Computer Science
Match the decay process (numbers 1-6 below) with a characteristic which is specific to that process (letters a-f below)
a) Formation of two heavy fragments; dominating decay mode for heaviest nuclei
b) Antineutrino emission occur simultaneously with this process
c) This emission process leaves the mass number unchanged but the atomic number will be reduced by one
d) Predominant mode of decay for neutron deficient nuclei with atomic number greater than 80
e) Does not ionize gases in Geiger counter so are often not counted by these devices; can be detected through fluorescence
f) Emitted particles are very dangerous as they cause extensive ionization of matter
1. Alpha decay
2. Beta decay
3. Positron decay
4. Electron capture
5. Gamma emission
6. Spontaneous fission
In: Chemistry
Name at least two DNA sequencing technologies and explain the principle.
Explain why organisms undergoing rapid evolutionary change often contain relatively large numbers of mobile DNA elements, whereas once organisms settle into a stable evolutionary niche, most of these mobile elements are lost.
What are the dominating taxonomic groups of microorganisms during a year cycle of a lake? Why?
In: Biology
Two stars of mass M1 and M2<M1 are orbiting eachother in a circular orbit. The heavy star experiences a supernova explosion, losing most of its mass in a spherically symmetric outflow (i.e. without losing angular momentum) and leaving behind a small neutron star of mass MNS. Show that if the mass lost is larger then half of the total mass of the system, the binary is disrupted.
In: Physics
A railroad car of mass 2.20 ✕ 104 kg moving at 5.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s.
(a) What is the speed of the three coupled cars after the
collision?
_________________m/s
(b) How much kinetic energy is lost in the collision?
________________J
In: Physics