Consider the network below with the following link travel time functions Xa is the flow (users) on link a; ta is the travel time of link a in minutes t₁(x1) = x₁ + 3 t₂(x2) = 2x2 + 1 t3(x3) = 3x3 t4(x4) = 22 t5(x5)= X5 1 2 X2 = C1D + c2 c1= c2= 5 3 3 4 Let D be the demand for the O-D pair (1, 4). (b) Assuming all paths are used at User-Equilibrium, express the link flow X2 as a function of D (Provide the values in 3 decimal places).

Find the line y = mx + b that best approximates the data points (0, 0), (1, 2), (2, 1) in the sense of least squares. Express the answer by giving mx + b, using syntax like (-1/3)*x-5 .

Get the local maximum and minimum points of the function

Find the minimum of Q = x2 + y2 if x + y = 6.

Assume SSE(b)=(8-4*b)^2+(10-3*b)^2 +(7-8*b)^2  . Find the value of b that will minimize this function.

A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.

Q1) A retail. Store stocks two types of shirts A and B. These are packed in attractive cardboard boxes. During a week the store can sell a maximum of 400 shirts of type A and a maximum of 300 shirts of type B. The storage capacity, however, is limited to a maximum of 600 of both types combined. Type A shirt fetches a profit of SR 2/- per unit and type B a profit of SR. 5/- per unit. (a) Formulate a mathematical model of the problem.

Find the maximum value of f(x) = - + 6

Model File Available: Major League Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, suppose the probabilities of Atlanta winning each game are as follows. Game Probability of Win 1 2 3 0.59 0.54 0.49 4 0.46 5 0.49 6 0.54 7 0.49 Construct a simulation model in which whether Atlanta wins or loses each game is a random variable. Use the model to answer the following questions. (Use at least 1,000 trials.) (a) What is the average number of games played regardless of winner? (Round your answer to one decimal place.) games (b) What is the probability that the Atlanta Braves win the World Series?…

Find the maximum and minimum of ?(?, ?) = 5? − 3?, subject to the constraint ?^ 2 + ?^ 2 = 136.