Consider a single server queuing model with Poisson arrivals (2 = 4/hour) and exponential service (u= 4/hour). The number in the system is restricted to a maximum of 10. The probability that a person who comes in leaves without joining the queue is
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- In this exercise we show that in the general case, exact recovery of a linear compression scheme is impossible. a. Let A ∈ Rn,d be anarbitrary compression matrix where n ≤ d−1. Show that there exists u,v ∈ Rd,u= v, such that Au = Av. Hint: Show that there exists u= 0,v = 0 such that Au = Av = 0. Hint: Consider using the rank-nullity theorem. b. Conclude that exact recovery of a linear compression scheme is impossible.Which of the following is not an assumption made when using the basic EOQ model? Select one: a. The order quantity is received all at once b. Lead time for the receipt of orders is constant c. Shortages are required d. Demand is known with certainty and is constant over timeMultiple DOF SystemsA 2-D spring-mass, frictionless system has the following parameters:m1 = 72m2 = 27k1 = 381k2 = 183x1,0 = 0 mx2,0 = 1 mv1,0 = -1 m/sv2,0 = 0 m/s In MATLAB, solve numerically for x1(t) and x2(t).
- A system has a characteristic equation s^3+2s^2+(k+1)s+8=0 Determine the range of K for a stable system Question 5 options: K<3 K<4 K>4 K>3Problem 7: On a hot day, the freezers in a particular ice cream shop maintain an average temperature of Tc = -11° C while the temperature of the surroundings is Th = 27° C.Randomized VariablesTc = -11° CTh = 27° C Part (a) Calculate the maximum coefficient of performance COP for the freezers. Part (b) If the work input to the freezer is W = 2.65 kJ and the freezer actually removes Qc = 7.8 × 103 J from the ice cream each second, what is the real coefficient of performance? Part (c) An employee puts m = 1.65 kg of melted ice cream at T0 = 3.5° C into the freezer. Assuming that the ice cream freezes at T1 = -1.0° C, how long in seconds will it take for the ice cream to reach its freezing temperature? Take the specific heat capacity of the melted ice cream as c = 4,000.0 J/(kg⋅K). Part (d) Assuming a latent heat of fusion of Lf = 280 kJ/kg, how long, Δt2, in seconds does it take to freeze the ice cream?A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?
- A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.Solve the following application problem: The model s(t) = -16?2 + 5? + 3 describes the height(in feet) of a diver at time ? is measured in seconds. Find the velocity of the diver when the diver hits the water.We are using simple exponential smoothing to predictmonthly electric shaver sales at Hook’s Drug Store. At theend of October 2006, our forecast for December 2006 saleswas 40. In November 50 shavers were sold, and duringDecember 45 shavers were sold. Suppose a 0.50. At theend of December, 2006, what is our prediction for the totalnumber of shavers that will be sold during March and Aprilof 2007?
- An unmanned submarine is equipped with temperature and depth measuring instruments and has radio equipment that can transmit the output readings of these instruments back to the surface. The submarine is initially floating on the surface of the sea with the instrument output readings in steady state. The depth measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 50 seconds. The water temperature on the sea surface, , is 20 °C and the temperature at a depth of x meters is given by the relation: If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 meters / second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading.What temperature does the submarine report at a depth of 1000 meters?For the Western Electric rule that if at least 2 of 3 consecutive points fall beyond 2σ to one side of the center line the process is out of control:a. FindtheType1errorrate.b. Find the Type 2 error rate if the process shifts from u to u + 2σ.The vertical cross section of an irrigation canal is modeled by f (x) = 5x2 / x2+ 4 where x is measured in feet and x = 0 corresponds to the center of the canal. Use the integration capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop the flow of water when the water is 3 feet deep?