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- 5 prove graphically (for strictly convex labor/leisure indifference curves) that workers can always be induced to work longer hours using overtime pay (time and a half) than with any straight hourly wage. [Hint begin with the wage w* that induces the most hours worked then show another wage w^ < w8 that will (when supplemented by overtime) induce worker to work more hoursDetermine the set of prices that would satisfy the condition of each the three markets using Gauss-Jordan method. Given following below in the picture.The dependencies between the 10 activities listed in the table above are as follows:• The project starts with two activities—A, and B—which can be done concurrently.• When activity A is finished, activity C can start• When activity B is finished, activities D and E can start• When both activities C and D are finished, activity F can start• When activity E is finished, activity G can start• When activity F is finished, activity H can start• When both activities G and H are finished, activity I can start• When activity G is finished, activity J can start• The project is complete when activities I and J are finished Questions1. Organize the information above in an activity precedence table showing the activity, precedent and duration (calculated using the PERT weighted average formula and round to the nearest integer).2. Draw an AON network diagram and calculate its early start, early finish, late start and late finish times, floats (Free and total) for each activity. Make sure you…
- Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and ofthis number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polishedusing the second polishing solution, and 196 lenses were satisfactory upon completion.(a) Is there any reason to believe that the two polishing solutions differ? Use α = 0.01A company is taking bids on four construction jobs. Their bids, in thousands of dollars, are given below. Job 1 Job 2 Job 3 Job 4 Contractor 1 50 46 42 40 Contractor 2 51 48 44 - Contractor 3 - 47 45 45 A dash indicates that the contractor did not bid on the given job. Contractor 1 can do only one job, but contractors 2 and 3 can each do up to 2 jobs. Determine the minimum cost assignment of contractors to jobs.John is a manager at a small English Bakery that sells gooseberry pies. Currently, each of his three employees, agent 1, agent 2 and agent 3, work independently on full commission. Assume to begin with that individual effort is observable, and that total output is given by Q = 10(E1 + E2 + E2). Agents are paid a salary of a + Qi (where Q1 = 10 E1 = output from agent 1; Q2 = 10E2 = output from agent 2 = 10E2 and so on). Each agent has an alternative utility level of 10 units, and the cost of effort C(E) = E2. Answer the following questions.a) Given this compensation scheme, what is the (privately) optimal amount of effort for agent 1?b) How many pies does she make?c) What must the fixed portion of agent 1’s income (a) be for her utility on this job to exactly equal 10?d) What is agent 1’s total income in the above situation?e) Check to see that agent 1’s utility level is in fact 10 when she gets this total income and chooses her effort optimally.f) What is the profit for the firm that…
- D. Find (with proof) the infimums of the sets S = {1 /n:n ∈ ℕ+} and T = { (-1)n / n : n ∈ ℕ+}. Is either infimum a minimum?SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.Course: StatisticsIn a company, 2 types of productivity bonuses have been assigned to best performing workers (A and B), consisting of 40% of their monthly income (A), a bonus of 15% of their monthly income (B) and those who are neither in A nor B must be trained in a maximum period of 6 months. According to this, 12% earned Bonus A, 29% Bonus B and rest must be trained. If number of workers is 1,200, which of following statement(s) is/are true?I. Number of employees to be trained is 708.II. Percentage of employees who must be trained AND also receive Bonus B is 87.7%.III. Number of employees receiving Bonus A is 144.Select one:a. Only Ib. Only IIc. I and IId. I and IIIe. I, II and III
- Find (with proof) the infimums of the sets S = {1 / n : n ∈ ℕ} and T = { (-1)n / n : n ∈ ℕ}. Is either infimum a minimum?Two lattice points (a,b) and (m,n) are mutually visible if and only if a−m and b−n are relatively primeSuppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…