Can you please provide a full solution for this problem Question 3 (12 marks)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,t]. The cost ofeach intervention is assumed to be proportional to the square of its intensity. Thus we formulate theoptimization problem below.Minimize the objective functionJ(u1(.), u2(.) = " A₁E(t) + A21(t) + B¹u²(t) + ¹²u²(t)1subject tod.S=dtdVA(1 p) BSI+kV-ds,=Ap-kVdV,dtdE=dtBSI (u(t) +e+d)E+OR,dI== EE (d-8-u2(t))I,dtdR= u(t)Eu₂(t) (d+0)RdtS(0) So≥0, V(0) = Vo≥ 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(t) b₁ and 0 < u2(t)

Answered: Question 3 (12 marks) We intend to…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
I am having troble interpreting these two tables.
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.
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.
Assume that a population of patients contains 30% of individuals who suffer from a certain fatal syndrome Z, which simultaneously makes it uncomfortable for them to take a life-prolonging drug X. Let Z = 1 and Z = 0 represent, respectively, the presence and absence of the syndrome, Y = 1 and Y = 0 represent death and survival, respectively, and X = 1 and X = 0 represent taking and not taking the drug. Assume that patients not carrying the syndrome, Z = 0, die with probability 0.5 if they take the drug and with probability 0.5 if they do not. Patients carrying the syndrome, Z = 1, on the other hand, die with probability 0.7 if they do not take the drug and with probability 0.3 if they do take the drug. Further, patients having the syndrome are more likely to avoid the drug, with probabilities p(X = 1|Z=0) = 0.9 and P(X = 1|Z = 1) = 0.6 . Based on this model, compute the joint distributions and for all values of x, y, and z. Present the following joint distributions in tables. [Hint:…
What is the significance of R and R2 in gression model?
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 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 S 1 {o if if advanced if aeroderivative and x4 X3 = not 0 if not Write a complete second-order model for heat rate (y ) as a function of cycle speed, cycle pressure ratio, and engine type.
7. a) What are residual plots and box plots? b) Do the stability analysis of the following model which is formulated to study the effect of toxicant on one competing species where the environmental toxicant concentration is being taken to change w.r.t. time. dN = rN, - α,Ν,N, - d,C,N , dt dN2 = rN, - α,N,., dt dCo = k,P - g,C, – m¡C, dt dP Q- hp – kPN, + gC,N . dt along with the initial conditions. N, (0) = N10,N2 (0)= N20,C, (0)= 0, P(0)= P, > 0 %3D Here, N1 (t) = Density of prey population
Calcium is the most abundant mineral in the human body and has several important functions. Most body calcium is stored in the bones and teeth, where it functions to support theirstructure. Recommendations for calcium are provided in Dietary Reference Intakes, developed by theInstitute of Medicine of the National Academy of Sciences. The recommended adequate intake (RAI) of calcium for adults (ages 19–50 years) is 1000 milligrams (mg) per day. Suppose that we want to perform a hypothesis test to decide whether the average adult with an income below the poverty level gets less than the RAI of 1000 mg.a. Determine the null hypothesis for the hypothesis test.b. Determine the alternative hypothesis for the hypothesis test.c. Classify the hypothesis test as two tailed, left tailed, or right tailed.
y y 90 54 50 53 80 91 35 41 60 48 35 61 60 71 40 56 60 71 55 68 40 47 65 36 55 53 35 11 50 68 60 70 65 57 90 79 50 79 35 59 A data set consist of dependent variable (y) and independent variable (x) as shown above. It is claims that the relationship between the x and y can be modelled through a regression model as follows: ŷ = a+bx where a and b are the estimated values for a and ß (refer to Appendix). (i) Determine the equation of the regression line to predict the y value from the x value. (ii) If the x value is 75, what is the value of y? (iii) Test the hypothesis that a=10 against the alternative a <10. Use a 0.05 level of significance. (iv) Construct a 95% prediction interval for the y with x=35.

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