Chap_04 - Business Decision Making and Management Science...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Chapter 4 - Linear Programming: Modeling Examples Chapter 4 Linear Programming: Modeling Examples Business Decision Making and Management Science
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 2
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.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
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!
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 6
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
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 8
9 Chapter 4 - Linear Programming: Modeling Examples Marketing Applications Media Selection Max 5000 X1 + 8500 X2 + 2400 X3 + 2800 X4 s.t.
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern