Show that Finco’s objective function may also be written as
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Operations Research : Applications and Algorithms
- The van der Waal's equation of state is given as RT a v-b v² For sulfur dioxide at temperature, T, of 300 K and a pressure, P, of 1 atm, the constants are given as: R = 0.08206 L.atm/(mol.K) L2.mol² P = a = 6.7689 atm.L b=0.05679 L.mol™¹ a) Plot the function f(v)=0 the for volumes for the range of 0 to 40 L/mol using 0.5 increment. b) Identify the root in this plot (where the curve crosses x-axis). c) Use the MATLAB function (fzero) to solve the original f(v) function for the specific volume using the initial guess from part (c). d) Use the MATLAB function (roots) to solve the original f(v) function for the specific volume.arrow_forwardFor the following three functions, write down truth tables for all of themand check if any two functions or all of them are equal or not. f=y՛z՛+x՛y+x՛yz՛g=xy՛+x՛z՛+x՛yh=(x՛+y՛)(x+y+z՛)arrow_forwardDESIGN ACTIVITY 3: GAUSS-NEWTON Fit the function f(x; ao, a1) = ap(1 - ea1k) to the data: 0.25 0.28 0.75 1.25 0.68 1.75 2.25 0.79 y 0.57 0.74 Use initial guesses of a, = 1.0 and a, = 1.0 for the parameters. Note that for these guesses, the initial sum of the squares of the residuals is 0.0248 Show your outputs in terms of the following: 1. Paper computation and solution 2. Excel data tabling 3. Matlab code w/ results Hint:The partial derivatives of the function with respect to the parameters are: af = 1-e-a1x dao af = agxe-a1x да,arrow_forward
- 2. Generate truth table for the following functions:(a) F(X,Y,Z)=∑(1,3,6,7)(b) F(X,Y,Z)=π(1,3,4)(c) F(W,X,Y,Z)=∑(1,4,7,10,12,15)(d) F(W,X,Y,Z)=π(2,3,4,7,10,11,12,13)arrow_forwardShow that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z havethe value 1.arrow_forwardA discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4arrow_forward
- A. Simplify the following Boolean functions: 1. F (x,y,z) = Em (2, 3, 4, 5) 2. F (x,y,z) = Em (3, 4, 6, 7) 3. F (A,B,C) = Em (0, 2, 4, 5, 6) %3D %3Darrow_forwardQ1/The pressure drop in pascals (Pa) for a fluid flowing in a pipe with a sudden decrease in diameter can be determined based on the loss of head equation given below: h = 24-11 2g Area A Area A Area A Where: V₂ is the velocity in position 2 (m/s), g: is acceleration due to gravity = 9.81 m/s², A₁ and A₂ are the cross-sectional areas of the tube in position 1 and 2 respectively. A==d² Where: d is the diameter (m). Write a program in a script file that calculates the head loss. When the script file is executed, it requests the user to input the velocity (V₂) in m/s and values of diameters (d, and d₂). The program displays the inputted value of v followed by a table with the values of diameters in the first and second columns and the corresponding values of h, in the third column. 2 2arrow_forwardThe electric flux density D at the point M (0,4,0) in the region about a uniform line charge of 1 nC/m lying along the z axis in free space is: Select one: a. None of the above b. 0.6366 nC/m c. 0.2387 nC/m d. 0.039 nC/m e. 0.1 nC/marrow_forward
- 11. Simplify the following Boolean functions using Karnaugh maps: а) F(x, y, z) = E(1, 2, 3, 5, 6, 7) F(x, y, z) = E(0, 1, 2, 3, 4, 6) F(x, y, z, t) = E(0, 2, 4, 6, 7, 8, 10, 11, 12, 14, 15) b) c)arrow_forwardTwo small charged objects attract each other with a force F when separated by a distance d.If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2,the force becomes?arrow_forwardA circle in the XY-coordinate system is specified by the center coordinates (x, y) and radius (r). Read the values for 2 circles- x1, y1, r1 for C1 and x2, y2, r2 for C2. (i) Determine whether the 2 circles intersect. To solve the problem it suffices to check if the distance between the 2 centers is lesser than the sum of radii of the 2 circles. (ii) Find the smallest circle that encloses the two circles and return its center coordinates and radius. programming language - carrow_forward
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