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

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.

5. The equation(s) required for applying the least squares method in the computation of fixed and variable production costs could be expressed as A. Exy = ax + b Ex? y = a + bx? Exy = na + b Ex C. Ey = na + b Ex D. Exy = a£x + b Ex? Ey = na + bEx В.

Osteoporosis is a degenerative disease that primarily affects women over the age of 60. A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales = β0 + β1Population + β2Income + ε, where Sales refers to the sales of StrongBones (in $1,000,000s), Population is the number of women over the age of 60 (in millions), and Income is the average income of women over the age of 60 (in $1,000s). She collects data on 38 cities across the United States and obtains the following regression results:     Coefficients StandardError t Stat p-Value Intercept 10.35 4.02 2.57 0.0199 Population 8.47 2.71 3.12 0.0062 Income 7.62 6.63 1.15 0.2661   a. What is the sample regression equation? (Enter your answers in millions rounded to 2 decimal places.)       b-1. Interpret the coefficient of population.  multiple choice 1 As the number of women over the age of 60 increases by 1 million, sales of StrongBones…

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.

How do we determine the types of the equilibrium points regarding their stability ?

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?

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Many manufacturing situations, for example, the production of such large and complex items as aircraft or machines, exhibit a learning effect in which the production time per unit decreases as more units are produced. This is often modeled by a power curve, y = ax , where a and b are constants. Suppose that the accompanying data on production times for the first ten units produced were collected from a new project at Glasgow Machine Tool. Develop a model for estimating the power curve to minimize the sum of the squared deviations of the errors. Use nonlinear optimization to find the parameters. Click the icon to view the production times data. The model is y=(x-D (Round to two decimal places as needed.) Get more help Production Times Data Unit Production Hours 1 2 3 4 5 6 7 8 9 10 Print 3,211.00 2,720.00 2,615.00 2,278.00 2,028.00 2,193.00 2,249.00 2,268.00 1,994.00 2,000.00 Done X [] Clear all Check answer