There are n tasks assigned to n workers, and each worker can be assigned only one task. Each worker can complete any one of the tasks, but the time spent varies. Use the ant colony algorithm to find the best allocation scheme that minimizes the total time spent. a) Build a mathematical model to describe the problem; b) Formulate state transition probability and pheromone update strategy;
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- Five workers are available to perform four jobs. The time it takes each worker to perform each job is given in the following table. The goal is to assign workers to jobs so as to minimize the total time required to perform the five jobs: Time Worker Job 1 Job 2 Job 3 Job 4 Job 5 1 10 15 10 15 16 2 12 8 20 16 14 3 12 9 12 18 22 4 6 12 15 18 8 5 16 12 8 12 8 Which worker should be assigned to which job? What is the total time required? (Hint: Use the Assignment model). If there are only 4 jobs (assume that job 5 is not required), how would the workers be assigned to jobs? (Hint: Change the constraints in the Assignment model).A private lake sells boating memberships and currently has 600 members. During the application process the potential members are asked which recreational activity they do the most. Their choices are fishing, skiing, boarding, swimming, or tubing. The lake manager chooses clients according to their interests to maximize the use of all areas of the lake. Every month, the lake rangers randomly sample the boats on the lake and categorize them according to the activity they are doing. The lake manager performs a chi-square goodness-of-fit test using the following null hypothesis to see whether their samples differ significantly from what the original applications claim. Ho Pfish =0.26, p,ki = 0.21, proard 0.21, Phoard 0.30, Psuim 0.12, Prube 0.11 In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples? A n> 30 B. 30 n< 50 46A private lake sells boating memberships and currently has 600 members. During the application process the potential members are asked which recreational activity they do the most. Their choices are fishing, skiing, boarding, swimming, or tubing. The lake manager chooses clients according to their interests to maximize the use of all areas of the lake. Every month, the lake rangers randomly sample the boats on the lake and categorize them according to the activity they are doing. The lake manager performs a chi-square goodness-of-fit test using the following null hypothesis to see whether their samples differ significantly from what the original applications claim. H0:pfish=0.26,pski=0.21,pboard=0.30,pswim=0.12,ptube=0.11 In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples? n≥30 lowercase n is greater than or equal to 30 A 30≤n≤50 30 is less than…personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting12workers randomly and timing each worker in each assembly process. Half of the workers are randomly chosen to use Process 1 first, and the rest use Process 2 first. The assembly time (in minutes) of each worker and each process is recorded, as shown in the table below. Worker process 1 process 2 Difference (Process 1 - Process 2) Send data to calculator 0 1 71 79 2 52 52 -8 0 3 49 43 6 4 41 58 - 17 5 6 fifty 76 40 49 10 27 7 (to) Formulate the null hypothesish and the alternative hypothesish 1. :0 89 83 6 8 70 84 9 74 67 -4 17 μ XI 10 eleven 12 Based on these data, can the company conclude, at the significance level of0.05, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test regardingμ (what isµwith…StarHortons Cup, the coffee company, wants to determine how long caffeine lasts throughout the day when individuals have a cup of one of their 3 types of coffee at 9am. They will then measure the levels of caffeine in these individuals’ systems at 10am, 12am, 2pm, 4pm, 6pm and 8pm. They want to have at least 20 observations per group. How many separate/distinct groups of participants are needed if they want to conduct this experiment using a mixed-measures ANOVA? 18 6 20 3Exercise 10.3.4: Selecting coders for 3 different projects. i About (a) A manager must select three coders from her group to write three different software projects. There are 7 junior and 3 senior coders in her group. The first project can be written by any of the coders. The second project must be written by a senior person and the third project must be written by a junior person. How many ways are there for her to assign the three coders to the projects if no person can be assigned to more than one project?Mateo believes that completely cutting caffeine out of a person's diet will allow them more restful sleep at night. He randomly selects 8 adults to help him test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days and then cut back to no caffeinated bevarages for an additional 28 days. During each period, the participants record the number of nights of restful sleep that they had. The following table gives the results of the study. Test Mateo's claim at the 0.05 level of significance. Give answers to 4 decimal places as needed. Number of Nights of Restful Sleep in a Four-Week Period 15 With Caffeine 21 20 22 24 18 21 24 20 26 26 22 21 23 27 23 Without Caffeine a) The normal probability plot showed the differences follow a normal distribution and the boxplot showed no outliers. b) Test the claim (1) Determine the null and alternative hypotheses. Enter correct symbol and values Ho: H₁: (2) Type of test: (3) a = (4) Test statistic (to) = p-value =…The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows. Number ofAssemblers One-HourProduction (units) 2 15 4 25 1 10 5 40 3 30 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Click here for the Excel Data File Draw a scatter diagram. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). Repeat the process for the remainder of the sample (No of…Draw the graph represented by the following adjacency matrix.In a lumberjack competition, a contestant is blindfolded and spun around 9 times. The blindfolded contestant then tries to hit the target point in the middle of a horizontal log with an axe. The contestant receives 15 points if his hit is within 3 cm of the target, 10 points if his hit is between 3 cm and 10 cm of the target, 5 points if his hit is between 10 cm and 20 cm of the target, and Zero points if his hit is 20 cm or more away from the target. Let Y record the position of the hit, so that Y=y>0 corresponds to missing the target point to the right by y cm Y=-y<0 corresponds to missing the target to the left by y cm. Assume that Y is normally distributed with mean mu=0 and variance 100 cm2. Find the expected number of points that the contestant wins.The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 11 during a one-hour period. Then 4 employees assembled them. They produced 18 during a one-hour period. The complete set of paired observations follows. Number ofAssemblers One-HourProduction (units) 2 11 4 18 1 5 5 23 3 18 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Click here for the Excel Data File Draw a scatter diagram. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). Repeat the process for the remainder of the sample (No of Assemblers2,…In a study, the effects of the mane of a male lion as a signal of quality to mates and rivals was explored. Four life-sized dummies of male lions provided a tool for testing female response to the unfamiliar lions whose manes varied by length (long or short) and color (blonde or dark). The female lions were observed to see whether they approached each of the four life-sized dummies. Complete parts (a) through (e) below. a. Identify the experimental units. Choose the correct answer below. The female lions The male dummies The mane colors The mane lengths Part 2 b. Identify the response variable. Choose the correct answer below. A. Whether or not (yes or no) the mane length affected how the female lions reacted to a male dummy. B. Whether or not (yes or no) the female lions approached the same dummies. C. Whether or not (yes or no) the female lions approached a male dummy. D. Whether or not…SEE MORE QUESTIONS