2.4.Use samplex method to solve the following goal programming problems:Z = P₁d₂¯+ P₂ (2d₂ ¯+ d3 ¯¯) + P3d₁*MinimizeSubject to constraintsx₁+x2+d₁-S₁ = 400X₁ +d₂= 240X2 +d3 = 300,X1, X2 d₁, d₁, d₂, d3 20Use Branch and Bound method to solve the following LPPMaximizeSubject to constraintsZ = 4x1 + 3x₂5x1 + 3x2≥ 30X₁4, x₂6i)ii)X₁, X₂0 and are integers.Consider a queueing system where arrivals are according to a poisson distribution withmeans. Find the expected waiting time in the system of the service time distribution isUniform from t-5 min to t-15 mins.Normal with mean 3 min and variance 4 min².

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
In a large city, researchers selected a random sample of 120 individuals who have multiple televisions in their house connected to a streaming device. Each individual was asked how many hours of streaming content they watch in a typical week. The sample had a mean of 12.5 hours. For which of the following populations is 12.5 hours a reasonable estimate of the mean hours of weekly streaming content watched? (A) All individuals who regularly watch streaming content (B) All individuals from this city who regularly watch streaming content (C) All individuals from this city with multiple streaming devices in their house (D) All individuals from this city with multiple streaming devices in their house who regularly watch streaming content (E) All 120 individuals in this city with multiple streaming devices in their home who regularly watch streaming content
From reviewing the temperature data for one of the regions of Iraq for a period of time, it was found that 15% of the days of the month of July (the number of days is 31) have a maximum temperature of more than 42 degrees Celsius and that 5% of the days of July have a temperature of less than 36 degrees Celsius. If you know that the temperature for the month of July in this region is subject to a normal distribution, then the mean and standard deviation S for this distribution are equal to:
5a.) Draw the graphs. Round your final answers up to 6 decimal places, if applicable. Give the correct units.
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in thedusLove uo useful life (150,000 miles of driving) of cars of a particular model varies Normall/ih nean 80 mg/mi and standard deviation 4 mg/mi. A company has 25 cars of this model in its et find the level L such that the probability that the average NOX+NMOG level 7 for the fleet is greater than L is only 0.01. Give your answer to three decimal places.
The life span of a certain wood cutting machine manufactured by a factory has a normal distribution with a guarantee that any machine that stars malfunctioning within 36 months of the purchase will be replaced by a new one. How many percentages of machines are expected to be replaced in the following cases? Mean of 60 months and variance of 64 months2 Mean of 45 months and variance of 36 months2 Mean of 75 months and variance of 16 months2
The average length of time for students to register in the second semester at a certain university has been 55 minutes. A new registration procedure is being tested. If random samples of 16 students have an average of 50 minutes with standard deviation of 12 minutes under system, can you conclude that the new system is faster than the old one? Assume that the average length of time is normally distributed. Use ά = 0.05.
The amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2, X3 each with a normal distribution. X1 has a mean µl =700 and standard deviation ơ1 55; X2 has mean u2 =700 and standard deviation o2 = 65; X3 has mean u3=900 and standard deviation 03 = 100. Suppose the prices per gallon are $2.90, $3.00 and $3.10 for X1, X2, and X3 respectively. Find the probability that the combined revenue for a given day is less than $6000. Use the z-score table. Round answer to the nearest hundredth.
A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 12 days yields the following return percentages.−1.81, 1.54, 1.52, −2.58, −2.3, 0.97, 0.93, −1.06, 1.04, 0.2, −0.63, −2.75 Send data to calculator If we assume that the returns are normally distributed, find a 90% confidence interval for the mean daily return on this stock. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: ? Upper limit: ?
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 1.0 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n = 11 customers in the first line and n2 = 30 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X1 and the mean service time for the longer one X2 is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i
Let Y be the life in hours of a battery. Assume Y is normally distributed with mean 200 and variance o?. If a purchaser of such batteries requires that at least 90% of the batteries have lives exceeding 150 hours, what is the largest value o can be and still have the purchaser satisfied?

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Consider a queueing system where arrivals are according to a poisson distribution with means. Find the expected waiting time in the system of the service time distribution is Uniform from t-5 min to t-15 mins. Normal with mean 3 min and variance 4 min². i) ii)