D 3.2-5. Use the graphical method to demonstrate that the fol- lowing model has no feasible solutions. Z = 5x, + 7x2, Maximize subject to 2x, - x2 < - 1 -x, + 2x2 < -1

The temperature on a sheet of metal is known to vary according to the following function: T(z,9) – 4z - 2ry We are interested to find the maximum temperature at the intersection of this sheet with a cylindrical pipe of negligible thickness. The equation of the intersection curve can be approximated as: 2+-4 Find the coordinates for the location of maximum temperature, the Lagrangian multiplier and the value of temperature at the optimum point. Wnite your answer with two decimal places of accuracy. HINT: IF there are more than one critical point, you can use substitution in the objective function to select the maximum. Enter your results here: Optimum value of z Optimum value of y Optimum value of A Optimum value of T

Find the solution for following nonlinear equation using Newton-Raphson method: f(x) = x^2+x+3"sin(x) and use -3 as the initial guess.

D 3.4-5. Consider the following problem, where the value of c, has not yet been ascertained. Maximize Z = c,x1 + 2xz, subject to 4x1 + x, < 12 X - x, 2 2 and X 20, X2 2 0. Use graphical analysis to determine the optimal solution(s) for (x1, X2) for the various possible values of c1.

%3! Q4: - For static system as shown in figure below, if k 50 N/mm, m =m2, u = 0.25 for the blocks m, and m2, tensions TI= 28.35N, spring elongation 5 mm and the force F1 m, cos 0 + m, sin 0. Find the inclination angle, Tension in other wire, and the mass of blocks. By using the Grammar method. T2 m2 T1 ml F1

11. g(x) = 2 In x- 6x - 4x 12. h(x) = e* Inx 13. y = Inx 14. f(x) = -4x log3 X 15. f(x) = e" log, x

P3.3: Reduce Fig. below to open loop form. R G, G2 G. HA H1

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Use the graphical method to find the optimal solution for the following LP equations: Min Z=10 X1 + 25 X2 Subject to X1220, X2 ≤40 ,XI +X2 ≥ 50 X1, X2 ≥ 0.

Q5: Solve the differential equation by using Laplace Transformation method? y" + 2y' + 2y = 5 y(0) = a, y'(0) = b %3D