Show that Finco’s objective function may also be written as
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Operations Research : Applications and Algorithms
- Convert the linear program problem into standard form. minimize 5x - 6y x - 2y = 7 -3x + 4y >= 8 x >= 0arrow_forward4 We consider the following initial value problem for two functions y(x),z(x): 0=y′′+(y′+6y)cos(z), 5z′=x^2+y^2+z^2, where 0≤x≤2 and y(0)=1.7, y′(0)=−2.7, z(0)=0.5. Approximate the solution of this initial value problem using Euler's method with 100 steps. (use Maple) What approximation value do you obtain for y(2) and z(1)?arrow_forwardGiven f(x) = 2x2+3x+1 and g(x) = 3x−2.Compute (a) (f◦g)(x) =arrow_forward
- Problem 1Write a MATLAB program for maximizing f(x) = x2 using genetic algorithm,where x ranges from 0 to 31. Perform 4 iterations.arrow_forwardUse the Quine McCluskey algorithm to simplify the function:F(w, x, y, z) = Σ(2, 6, 9, 10, 11, 13, 14, 15)Show all work – no credit will be given for an answer without accompanying workarrow_forwardLet S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function: S = 35L0.40 0.60 In this formula L represents the units of labor Input and C the units of capital input. Each unit of labor costs $150, and each unit of capital costs $200. a. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost. If the constant is "1" it must be entered in the box; if your answer is zero, enter "0". Min s.t. L C L, C b. Solve the optimization problem you formulated in part (a). Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5000 for both L and C before solving. Round your answers for L and C to three decimal places. Round your answer for optimal solution to one decimal place. L= and C= for an optimal solution of $. Please do…arrow_forward
- Applying Manhattan distance solve the following 8 puzzzle problem Initial state 1 2 3 4 8 7 6 5 goal state 1 2 3 4 5 6 7 8arrow_forwardA pulse radar system transmits 100 kW power through an isotropic antenna and receives 1 mW power. Assume ? = 1 m2 and operating frequency=1 GHz.a) What is the range of the target?b) Discuss, mathematically, how you can increase the range by a factor 2 without changing theabovementioned radar figures.arrow_forwardConsidering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point iteration. Assume an initial guess of 1. Use the equation form that will seem fit according to the choices provided.Group of answer choices 0.72210 0.71537 0.76396 0.72236arrow_forward
- The tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable. Basic Z 0 -5 0 4 -1 -10 0 0 598 0 3 0 -2 -3 -1 5 1 12 0 1 1 3 1 0 3 0 6 1 -1 0 0 6 -4 0 0 0 Categorize the variables as basic and nonbasic and provide the current values of all the variables. AP [8] Assuming that the problem is of the maximization type, identify the nonbasic variables that have the potential to improve the value of If each such variable enters the basic solution, determine the associated leaving…arrow_forwardGive 2 examples of the optimization problem and identify the following for each problem: Objective Function Design Variable Constraintarrow_forwardYou are given some tasks of size xK, yK and zK respectively and there are at most 9 tasks each. Determine the best that you could achieve if you are to fill up a hole of size SK, for the following values of x, y, z and S, by maximizing the space used (up to S), i.e. minimizing the used space, if any. Show how many tasks of size x, how many tasks of size y and how many tasks of size z are used in each of the three cases. (g) Now if we relax the requirement so that there are no upper limits on the number of tasks for each type, determine the maximal space usage and the task mix. (h) If we tighten the requirement so that there are still at most 9 tasks of each size, but we also require that each type of tasks must be used at least once, determine maximal space usage and the task mix. Case 1 2 3 X 22 26 28 y 33 43 65 50 77 74 S 488 556 777 You could complete the following table. Fill in the number of tasks inside the brackets and the corresponding maximal usage. (At most 9 tasks each (g)…arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole