KINDLY PROVIDE FULL DETAILS AND CALCUTLATIONS WITH ANSWERS AND NOT JUST HOW TO DO IT We intend to design a system for optimal control (u₁(t), u2(t)) which represent the Tuberculosis (TB)treatment rates for latent class and infectious class, respectively. Our target is to minimize the TBinfected individuals (including latent and infectious individuals) as well as the costs required to con-trol TB by treating latent and infectious individuals, over a certain time horizon [0,tf]. The cost ofeach intervention is assumed to be proportional to the square of its intensity. Thus we formulate theoptimization problem below.Minimize the objective function' A₁E(t) + A₂I(t) + ¹¹³u²(t) + Bu²(t)J(u(.)), u(·) = "h1subject todS=A(1p) BSI+ kV - ds,dtdVdtdEུ|ཙ⪜ཊྛི|༴ཁྱི|ཙdtdt= Ap-kV - dV,=BSI - (u(t) ++ d)E + OR,dR=E-(d--u2(t))I,= u₁(t)Eu(t) (d+ 0)RS(0) = So≥0, V(0) = √≥0, E(0) = Eo ≥0,1(0) = 10 ≥0, R(0) = Ro≥ 0.The control variables are assumed to be bounded: Given any t > 0,0

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Answered: We intend to design a system for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y , heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • X2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables S 1 0 if not { if advanced 1 if aeroderivative X3 = and X4 if not If the engine type is traditional, then x3 = and x4 When you plug in these two values in the complete second-order model equation, you will get the model equation for traditional engine type.
A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y, heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • x2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables (1 if advanced X3 = 0 if not {o 1 and X4 = ここ if aeroderivative 0if not There are 67 observations in the dataset. We conduct a global F-test for overall model adequacy at a level of significance 5%. 1. Numerator degrees of freedom 2. Denominator degrees of freedom 3. If F-value equals to 30.52, then we (reject or fail to reject) the null hypothesis at 5%. There is (sufficient or insufficient) that the complete second-order model is overall useful.
A study of a high-pressure inlet fogging method for a gas turbine engine analyzed a complete second-order model for y , heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of two quantitative variables • x1 , cycle speed (revolutions per minute) • X2 , cycle pressure ratio and a qualitative predictor, engine type, at three levels (traditional, advanced, and aeroderivative). We define two dummy variables 1 if advanced 3o if not if aeroderivative 3o if not X3 = and x4 = Write the model equation for advanced engine type.
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.
A company named FoodEX produces 200 kg of a feed composition consisting of two ingredients y1 and y2. The ingredient y1 costs Rs. 6 per kg and y2 costs Rs. 16 per kg. Not more than 80 kg of y1 can be used and atleast 60 kg of y2 must be used. The company wants to find how much of each ingredient should be used in the mix if it wants to minimize cost. You have to a) Develop the LP Model for this problem and find it's Dual. b) Find the solution of the Dual problem using Simplex Method. c) Perform the Sensitivity analysis of Basic and Non Basic Variables. Also find the shadow price of the resources.
We intend to design a system for optimal control (u₁(t), u2(t)) which represent the Tuberculosis (TB) treatment rates for latent class and infectious class, respectively. Our target is to minimize the TB infected individuals (including latent and infectious individuals) as well as the costs required to con- trol TB by treating latent and infectious individuals, over a certain time horizon [0,tf]. The cost of each intervention is assumed to be proportional to the square of its intensity. Thus we formulate the optimization problem below. Minimize the objective function ' A₁E(t) + A₂I(t) + ¹¹³u²(t) + Bu²(t) J(u(.)), u(·) = "h 1 subject to dS = A(1p) BSI+ kV - ds, dt dV dt dE ུ|ཙ⪜ཊྛི|༴ཁྱི|ཙ dt dt = Ap-kV - dV, = BSI - (u(t) ++ d)E + OR, dR = E-(d--u2(t))I, = u₁(t)Eu(t) (d+ 0)R S(0) = So≥0, V(0) = √≥0, E(0) = Eo ≥0,1(0) = 10 ≥0, R(0) = Ro≥ 0. The control variables are assumed to be bounded: Given any t > 0, 0
How do we determine the types of the equilibrium points regarding their stability ?
The company wants to find its daily production program maximizing its daily sales. These are made up of sales from individual types of fumiture. The company will receive CZK 500 for each chair produced, CZK 1,500 for a dining table and CZK 3,000 for each bed. Daily furniture production is stored in a warehouse with a size of 220 m2 The chairs occupy 0.5 m2, dining tables 2 m2 and beds 4 m2. The production of one chair takes 1 hour of work, the production of a dining table takes 2 hours and the bed takes 5 hours to produce due to its complexity. In total, there is a working hours capacity corresponding to the number of employees Long-term contracts with customers require that at least 10 beds be made per day. How much of chairs, dinning tables and beds have to be optimally produced daily ?
A price-taking firm has a production function given by
In the least-squares line ŷ = 5 + 9x, what is the marginal change in ŷ for each unit change in x?
Find the least-squares regression line fitting the data (x1,y1) = (1,1), (x2, y2) = (-2,-1), and (x3, y3) = (3,2). =
A firm produces output y from inputs x1 and x2 whose prices are given as w1 = 1 and w2 = 1 respectively. The production function is y = x11/2 x21/2 a) Write the Lagrangian function b) Find the firm’s cost function If you could write out the steps to the first part about how you got the function, that would be great. It would help me understand it.

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