QABE_Notes13

# QABE_Notes13 - QABE Lecture 13 Linear Programming III Using...

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QABE Lecture 13 Linear Programming III: Using Solver School of Economics, UNSW 2011 Contents 1 Introduction 1 2 The Problem 2 2 . 1 S e t t ingupth eP rob l em . ........................... 2 3 Using Solver 4 4 Changing the Objective Function: Multiple Solutions 11 1 Introduction In the past two lectures we have seen how to set up a linear programming problem and solve it using the graphical method. The Microsoft Excel program oFers us an

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ECON 1202/ECON 2291: QABE c ± School o fEconomics, UNSW 2T h e P r o b l e m Example: REVCO Motor Company REVCO motor company has two engine-manufacturing plants in Sydney, plants A and B, producing the 2-litre clean burning engine used in their new car model. The maximum production capacity of plants A and B are 50 engines and 55 engines per month respectively. The car engines are sent by road to the 2 car assembly plants of the company, one in Adelaide and one in Melbourne. The transport costs per engine from plant A in Sydney to Adelaide and Melbourne are \$100 and \$60 respectively while the transport costs per engine from plant B in Sydney to Adelaide and Melbourne are \$120 and \$70 respectively. In a given month, the Adelaide car assembly plant requires 40 engines while the Melbourne car assembly plant requires 35 engines. In satis- fying the engine requirements of the assembly plants in Adelaide and Melbourne, the objective of the company is to minimise the transport costs of the engines from Sydney to the 2 assembly plants in Adelaide and Melbourne. How many engines should be sent to each plant if cost is to be minimised? You can try working this out by hand if you like, but let’s try another way. First, we need to set the problem up. 2.1 Setting up the Problem Defne the Variables How do we set up this problem using the least number of variables? x = number sent from Plant A to Adelaide. y = number sent from Plant A to Melbourne. If 40 engines are required in Adelaide then 40 x engines must come from Plant B. If 35 engines are required in Melbourne then 35 y engines must come from Plant B. Objective Function and Constraints The objective function is: QABE Lecture 13 2
ECON 1202/ECON 2291: QABE c ± School o fEconomics, UNSW Transport Cost C = 100 x + 120(40 x )+60 y + 70(35 y ) = 100 x + 4800 120 x +60 y + 2450 70 y = 20 x 10 y + 7250 The constraints are: Capacity of Plant A: x + y 50 Capacity of Plant B: (40 x )+(35 y ) 55 x y ≤− 20 x + y 20 And: x

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QABE_Notes13 - QABE Lecture 13 Linear Programming III Using...

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