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**Homework Solution GOAL PROGRAMMING**

SHAWHAN FILE WORKS MGMT E-5050 Geraldine Shawhan is president of a firm that manufactures two types of metal file cabinets. Demand for her 2-drawer model is up to 600 weekly, while demand for her 3-drawer model is limited to 400 weekly. The firm has a weekly operating capacity of 1,300 hours, with the 2-drawer cabinet taking 1 hour to produce and the 3-drawer cabin- et requiring 2 hours. Each 2-drawer model yields a $10.00 profit, while the profit for the large model is $

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**Homework Solution GOAL PROGRAMMING**

SHAWHAN FILE WORKS Shawhan has listed the following goals in order of importance: Attain a profit as close to $11, as possible each week. Avoid underutilization of the firm’s production capacity. Sell as many 2-drawer cabinets and 3-drawer cabinets as the demand indicates. REQUIREMENT: Formulate the goal programming model. Solve this problem on QM for WINDOWS.

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**Homework Solution GOAL PROGRAMMING Let :**

SHAWHAN FILE WORKS Let : X1 = number of 2-drawer cabinets produced weekly X2 = number of 3-drawer cabinets produced weekly d1 = underachievement of profit goal d1 = overachievement of profit goal d2 = idle time in production capacity d3 = underachievement of sales goal for 2-drawer cabinets d4 = underachievement of sales goal for 3-drawer cabinets - + - - -

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**Homework Solution GOAL PROGRAMMING - - - -**

+ Minimize deviations = P1d1 + P1d1 + P2d2 + P3d3 + P3d4 subject to : - + 10X1 + 15X2 + d1 – d1 = $11, ( profit target ) 1X X2 + d2 - d2 = 1,300 hours ( production limit ) 1X d3 - d3 = ( 2-drawer sales limit ) 1X d4 - d4 = ( 3-drawer sales limit ) - + - + - + All Xi , di variables => 0

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**Goal Programming with QM for WINDOWS**

Shawhan File Works

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**1st Goal, 1st Priority : Profit should be as close to $11,000**

1st Goal, 1st Priority : Profit should be as close to $11,000. as possible 2nd Goal, 2nd Priority : Avoid underutilization of production capacity 3rd Goal, 3rd Priority : Sell as many 2-draw cabinets as demand states 3rd Goal, 3rd Priority : Sell as many 3-draw cabinets as demand states

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Priority 3 3rd

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**Homework Solution THE CAMPAIGN MANAGER GOAL PROGRAMMING**

The campaign manager for a politician who is running for reelection is currently engaged in the planning process. Four ways to advertise have been selected: television ads, radio ads, billboards, and newspa- per ads. The costs are as follows: - $ for each television ad - $ for each radio ad - $ for a billboard for one month - $ for each newspaper ad The audience reached by each type of advertising has been estimated at: - 40,000 for each television ad - 32,000 for each radio ad - 34,000 for each billboard - 17,000 for each newspaper ad The total monthly advertising budget is $16,000.00

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THE CAMPAIGN MANAGER Homework Solution The following goals have been established and ranked: The number of people reached should be at least 1,500,000. The total monthly advertising budget should not be exceeded. Together, the number of ads on either television or radio should be at least six (6). No more than ten (10) ads of any type of advertising should be used. REQUIREMENT: Formulate this as a goal programming problem. Solve this problem via QM for WINDOWS. Which goals are completely met and which of them are not?

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**Homework Solution GOAL PROGRAMMING**

THE CAMPAIGN MANAGER Homework Solution GOAL PROGRAMMING Let : X1 = the number of television ads X2 = the number of radio ads X3 = the number of billboard ads X4 = the number of newspaper ads Subject to : (1) the number of people reached. (2) the budget. (3) the number of TV or radio ads. (4) restriction on the number of each individual type of ad.

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THE CAMPAIGN MANAGER Homework Solution Minimize deviations = P1d1- + P2d2+ + P3d3- + P4d4+ + P4d5+ P4d6+ + P4d7+ subject to : The number of people reached: 40,000 X1 + 32,000 X2 + 34,000 X3 + 17,000 X4 –d1+ + d1- = 1,500,000 The budget: 900 X X X X4 –d2+ + d2- = 16,000 The number of television or radio ads: X1 + X2 –d3+ + d3- = 6 Restriction on the number of each individual type of ad: X1 – d4+ + d4- = X3 –d6+ + d6- = 10 X2 – d5+ + d5- = X4 –d7+ + d7- = 10 X1 , X2 , X3, X4 , and all di => 0 non-negativity constraint

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**Homework Solution SUMMARY The number of television ads = 0**

THE CAMPAIGN MANAGER Homework Solution SUMMARY The number of television ads = 0 The number of radio ads = .73 ≈ 0 The number of billboard ads = 0 The number of newspaper ads = 88.86 The number of newspaper ads was exceeded by 78.86 Goal #1 – the number of people reached was met exactly. Goal #2 – the budget of $16, was met ($15,994.80) Goals #3 and #4 – not met ; the number of television, radio, and billboard ads are each less than 10.

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**Goal Programming with QM for WINDOWS**

The Campaign Manager

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**88.86 newspaper ads @ $180.00 = $15,994.80 88.86 newspaper ads**

3 88.86 newspaper ads @ 17,000 people reached = 1,510,620 people Audience exposure and budget are met completely. The number of TV, radio, and billboard ads are each less than 10. The other goals are not met.

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Chapter 3 Linear Programming Applications

Chapter 3 Linear Programming Applications

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