Chap_04 - Business Decision Making and Management Science...

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1 Chapter 4 - Linear Programming: Modeling Examples Chapter 4 Linear Programming: Modeling Examples Business Decision Making and Management Science

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2 Chapter 4 - Linear Programming: Modeling Examples Financial Applications Portfolio Selection International City Trust (ICT) International City Trust (ICT) ICT has \$5 million available for immediate investment and wishes to do two things: (1) maximize the interest earned on the investments made over the next six months, and (2) satisfy the diversification requirements as set by the board of directors.
3 Chapter 4 - Linear Programming: Modeling Examples Financial Applications Portfolio Selection International City Trust (ICT) International City Trust (ICT) Also, the board specifies that at least 55% at least 55% of the funds invested must be in gold stocks and construction loans, and that no less than 15% no less than 15% be invested in trade credit.

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4 Chapter 4 - Linear Programming: Modeling Examples Financial Applications Portfolio Selection International City Trust (ICT) International City Trust (ICT) Formulate ICT’s decision as an LP problem. Let Let X 1 = dollars invested in trade credit X 2 = dollars invested in corporate bonds X 3 = dollars invested in gold stocks X 4 = dollars invested in construction loans
5 Chapter 4 - Linear Programming: Modeling Examples Financial Applications Portfolio Selection LP Model for International City Trust (ICT) LP Model for International City Trust (ICT) Max Z = 0.07X 1 + 0.11X 2 + 0.19X 3 + 0.15X 4 s.t.: X 1 ≤ 1,000,000 X 2 ≤ 2,500,000 X 3 ≤ 1,500,000 X 4 ≤ 1,800,000 X 3 + X 4 ≥ 0.55(X 1 +X 2 +X 3 +X 4 ) X 1 ≥ 0.15(X 1 +X 2 +X 3 +X 4 ) X 1 + X 2 + X 3 + X 4 ≤ 5,000,000 X 1 , X 2 , X 3 , X 4 ≥ 0 SOLUTION: SOLUTION: X 1 = \$750,000, X 2 =\$950,000, X 3 = \$1,500,000, and X 4 = \$1,800,000.Total interest earned = \$712,000 Ratio Constraints!

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6 Chapter 4 - Linear Programming: Modeling Examples Marketing Applications Media Selection Linear programming models have been used in the advertising field as a decision aid in selecting an effective media mix. Media selection problems can be approached with LP from two perspectives. The objective can be - to maximize audience exposure or - to minimize advertising costs.
7 Chapter 4 - Linear Programming: Modeling Examples Medium Audience Reached Per Ad Cost Per Ad(\$) Maximum Ads Per Week TV spot (1 minute) 5,000 800 12 Daily newspaper, full page ad) 8,500 925 5 Radio spot (30 seconds, PT) 2,400 290 25 Radio spot (1 minute, afternoon) 2,800 380 20 Marketing Applications Media Selection

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8 Chapter 4 - Linear Programming: Modeling Examples The total budget is \$8,000. The contractual arrangements require that at least 5 radio spots be placed each week. Management insists that no more than \$1,800 be spent on radio advertising every week. Let Let X X 1 = = # of 1-minute TV spots each week X X 2 = = # of daily paper ads each week X X 3 = = # of 30-second radio spots each week X X 4 = = # of 1-minute radio spots each week Marketing Applications Media Selection
9 Chapter 4 - Linear Programming: Modeling Examples Marketing Applications Media Selection Max 5000 X1 + 8500 X2 + 2400 X3 + 2800 X4 s.t.

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