MATLAB question!

4. (a) Modify the code, to compute and plot the quantity E = 1/2mv^2 + 1/2ky^2 as a function of time. What do you observe? Is the energy conserved in this case?

(b) Show analytically that dE/dt < 0 for c > 0 while dE/dt > 0 for c < 0.

(c) Modify the code to plot v vs y (phase plot). Comment on the behavior of the curve in the context of the motion of the spring. Does the graph ever get close to the origin? Why or why not?

given code
---------------------------------------------------------------

clear all;   
m = 4; % mass [kg]
k = 9; % spring constant [N/m]
c = 4; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 =-0.8; v0 = 0.3; % initial conditions
[t,Y] = ode45(@f,[0,15],[y0,v0],[],omega0, p); % solve for 0<t<15
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'ro-',t,v,'b+-');% time series for y and v
grid on; axis tight;
%---------------------------------------------------
function dYdt = f(t,Y,omega0,p); % function defining the DE
y = Y(1); v = Y(2);
dYdt=[ v ; -omega0^2*y-2*p*v]; % fill-in dv/dt
end

-----------------------------------------------------------------------------------------

60 % of the chips used by a computer manufacturing company (CMC) are provided by supplier A and the rest by supplier B. The two suppliers have the following faulty chip rates: 0.3% for supplier A and 0.8% for supplier B. Consider a random batch of 20 chips (chips cannot be distinguished by supplier). a. Show that the expected number of faulty chips is 0.1. [15 marks] b. What is the probability of having two or more faulty chips? Justify your answer and the choice of the probability distribution. [15 marks] If the daily production of computer is 1000, and each computer has one chip: c. What is the probability that 8 or more computers do not pass the final quality check due to faulty chips? Justify your approach. [20 marks] The company, CMC, has to decide whether to implement a quality control screening of chips when delivered by the suppliers. In this case, only the chips that pass the screening will be used in the production process. Previous experience of quality control screenings reported that in 95% of the cases it was able to correctly identify faulty chips and in 3% of the cases was giving false negatives (meaning that even though the chip was working correctly the screening identified it as faulty). The screening process will be convenient only if the average number of daily faulty computers will be smaller than 3. d. Should the company implement the quality control screening? [20 marks]

60 % of the chips used by a computer manufacturing company (CMC) are provided by supplier A and the rest by supplier B. The two suppliers have the following faulty chip rates: 0.3% for supplier A and 0.8% for supplier B. Consider a random batch of 20 chips (chips cannot be distinguished by supplier). a. Show that the expected number of faulty chips is 0.1. [15 marks] b. What is the probability of having two or more faulty chips? Justify your answer and the choice of the probability distribution. [15 marks] If the daily production of computer is 1000, and each computer has one chip: c. What is the probability that 8 or more computers do not pass the final quality check due to faulty chips? Justify your approach. [20 marks] The company, CMC, has to decide whether to implement a quality control screening of chips when delivered by the suppliers. In this case, only the chips that pass the screening will be used in the production process. Previous experience of quality control screenings reported that in 95% of the cases it was able to correctly identify faulty chips and in 3% of the cases was giving false negatives (meaning that even though the chip was working correctly the screening identified it as faulty). The screening process will be convenient only if the average number of daily faulty computers will be smaller than 3. d. Should the company implement the quality control screening? [20 marks]

PLEASE READ: This is one question with 3 parts to it, please answer the full question.

Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20 percent above suggest retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation. There are two possible sites under consideration. One is relatively small, while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $ 200,000. If demand is low, he will lose $180,000. If he opens at Site 2 and demand is high, he will generate a profit of $100,000, but he will lose $20,000 if demand is low. He also has the option of not opening either. He believes that there is a 50 percent chance that demand will be high. Mark can purchase a market research study from Brooklyn College. The survey costs $10,000. The probability of a good demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.3. There is a 45 percent chance that the study will be favorable. Draw a decision tree to determine the following:

a)What should Mark’s decisions be?

b)What is the maximum amount Mark should be willing to pay for this study?

c)What is the efficiency of the study?

Hint: The revised probabilities have already been calculated for you.

Based on these Common-size Income Statements for Nike for the periods shown, which of the following statements is most accurate?

Nike's net profit margin rose from 2011 to 2015, largely due to a declingin Cost of Sales percentage.

Nike's net profit margin rose from 2011 to 2015, most likely because of increasing Sales over that period.

Nike produced lower profit from each dollar of Sales in 2015 than in 2011, mostly due to an increase in its effective income tax rate.

Nike's overall profitability rose from 2011 to 2015, mostly due to relative decreases in its interest payments and SG&A expenses.

Prospective drivers who enrol in Smart Driver Driving School have always been taught by a conventional teaching method. The driving school has many branches across provinces. Last year, among all students that took driving lessons from the school in a certain province, 80% passed the provincial road test. This year, the teaching committee came up with a new teaching method. The committee randomly assigned half of its 2400 students enrolled this year to receive the conventional teaching method and the remaining half to receive the new teaching method. In a random sample of 100 students who received the conventional teaching method, 79% passed the road test.

Part i) To test if the passing rate has decreased from last year for students who received the conventional teaching method, what will be the null hypothesis?

A. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.79.
B. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.
C. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.
D. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.
E. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year equals 0.79.
F. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.

Part ii) For the test mentioned in the previous part, what will be the alternative hypothesis?

A. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year equals 0.79.
B. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.
C. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.79.
D. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.
E. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.
F. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.

Part iii) What is the approximate null model for the sample proportion of the conventional teaching group who passed the road test?

A. ?(0.80, √0.8⋅0.21/200)
B. ?(0.80, √0.8⋅0.2/100)
C. ?(0.79, √0.79⋅0.21/100)
D. ?(0.79, √0.8⋅0.2/100)
E. ?(0.80, √0.79⋅0.21/100)
F. ?(0.79, √0.79⋅0.21/1200)

Part iv) Compute the P-value: (your answer must be expressed as a proportion and rounded to 4 decimal places.)

Part v) What is an appropriate conclusion for the hypothesis test at the 2% significance level?

A. The passing rate for students taught using the conventional method this year is significantly lower than last year.
B. The passing rate for students taught using the conventional method this year is not significantly lower than last year.
C. The passing rate for students taught using the conventional method this year is the same as last year.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory. In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months: Month 1 2 3 4 Quality control measures: Number of defects 194 172 133 94 Number of warranty claims 55 48 39 36 Number of customer complaints 111 105 88 67 Material control measures: Purchase order lead time 8 days 7 days 5 days 4 days Scrap as a percent of total cost 1 % 1 % 2 % 3 % Machine performance measures: Machine downtime as a percentage of availability 5 % 6 % 6 % 10 % Use as a percentage of availability 94 % 91 % 88 % 84 % Setup time (hours) 8 10 11 12 Delivery performance measures: Throughput time ? ? ? ? Manufacturing cycle efficiency (MCE) ? ? ? ? Delivery cycle time ? ? ? ? Percentage of on-time deliveries 95 % 94 % 91 % 88 % The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures: Average per Month (in days) 1 2 3 4 Wait time per order before start of production 10.0 12.6 13.0 15.0 Inspection time per unit 0.9 0.8 0.8 0.8 Process time per unit 2.8 2.4 2.2 1.3 Queue time per unit 3.9 4.6 5.4 7.2 Move time per unit 0.4 0.6 0.6 0.7

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.