Resource Allocation Problem Statement The type of problem most often identified with the application of linear program is the problem of distributing scarce resources among alternative activities. The Product Mix problem is a special case. In this example‚ we consider a manufacturing facility that produces five different products using four machines. The scarce resources are the times available on the machines and the alternative activities are the individual production volumes. The machine
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Algorithm to Calculate Basic Feasible Solution using Simplex Method Abstract: The problem of maximization/minimization deals with choosing the ideal set of values of variables in order to find the extrema of an equation subject to constraints. The simplex method is one of the fundamental methods of calculating the Basic Feasible Solution (BFS) of a maximization/minimization. This algorithm implements the simplex method to allow for quick calculation of the BFS to maximize profit or minimize loss
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Case Problem 3: Hart Venture Capital 1. Let S = fraction of the Security Systems project funded by HVC M = fraction of the Market Analysis project funded by HVC Max 1‚800‚000S + 1‚600‚000M s.t. 600‚000S + 500‚000M ≤ 800‚000 Year 1 600‚000S + 350‚000M ≤ 700‚000 Year 2 250‚000S + 400‚000M ≤ 500‚000 Year 3 S
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LOGISTICS Example how to use software transformation mode>new: 1.sources: number of source 2.destination:number of destination 3.activities minimize/maximize >click ok> supply‚ demand‚ time ________________________________________________________________________________________ logistics is a part of supply chain management‚ cooperation of different elements of different ownerships supply chain units do not compete with each other‚ but work as one body order cycle time-time
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SOLUTION TO ANDREW–CARTER‚ INC.‚ CASE This case presents some of the basic concepts of aggregate planning by the transportation method. The case involves solving a rather complex set of transportation problems. Four different configurations of operating plants have to be tested. The solutions‚ although requiring relatively few iterations to optimality‚ involve degeneracy if solved manually. The costs are: [pic] The lowest weekly total cost‚ operating plants 1 and 3 with 2 closed‚ is
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DEPARTMENT OF APPLIED MATHEMATICS BSc Honours in Operations Research and Applied Statistics SMO 1101 Introduction to Operations Research TUTORIAL QUESTIONS 1. List and discuss the six major steps in the quantitative modeling process. 2. What is the difference between a i. descriptive and a normative model? ii. discrete and a continuous variable? 3. Show that the set ℜ n is a convex set. 4. Is the linearity assumption‚ in LP models‚ realistic in applications? 5. Print-Rite assembles printers for personal
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Short Info On Excel Solver Excel Solver is a tool to model and solve linear and nonlinear programming problems. To access it‚ open Excel‚ choose the tab “Data” and select “Solver” from the “Analysis” group. If it is not there‚ you have to install it‚ by clicking the “File” tab (or the Office button)‚ then “Options”‚ then “Add-Ins”‚ and then “Manage Add-Ins”. Check “Solver” there. To solve the model‚ you have to first program in on a spreadsheet. In the attached “excel-example.xls” we solve the linear
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Attempt Score 34 out of 40 points Question 1 2 out of 2 points If exactly 3 projects are to be selected from a set of 5 projects‚ this would be written as 3 separate constraints in an integer program. Answer Selected Answer: False Correct Answer: False . Question 2 2 out of 2 points Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Answer Selected
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A: Formulation of the LP Model X1(Pizza)‚ X2(hotdogs)‚ X3(barbecue sandwiches) Constraints: Cost: Maximum fund available for the purchase = $1500 Cost per pizza slice = $6 (get 8 slices) =6/8 = $0.75 Cost for a hotdog = $.45 Cost for a barbecue sandwich = $.90 Constraint: 0.75X1 + 0.45X2+ 0.90(X3) ≤ 1500 Oven space: Space available = 3 x 4 x 16 = 192 sq. feet = 192 x 12 x 12 =27648 sq. inches The oven will be refilled before half time- 27648 x 2 = 55296
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The three products/variables in this problem that must be considered for purchase are: x1: Pizza Slices x2: Hot Dogs x3: Barbeque Sandwiches The objective is for Julia to maximize profits. Julia’s goal is to earn a profit of at least $1‚000.00 after each game. Profit = Sell – Cost Profit Function: Z = 0.75(X1) + 1.05(X2) + 1.35(X3) Constraints and Cost: The maximum amount of funds available for purchase is $1500.00 Cost per pizza slice = $0.75 because Julia purchases each pizza for $6.00
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