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Linear Programming: The Filing Cabinet Dilemma: Algebra 2

Linear Programming: The Filing Cabinet Dilemma: Algebra 2. MathScience Innovation Center Betsey Davis. Statement of Dilemma. Note: Algebra 2 Solution #22 page 167.

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Linear Programming: The Filing Cabinet Dilemma: Algebra 2

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  1. Linear Programming:The Filing Cabinet Dilemma:Algebra 2 MathScience Innovation Center Betsey Davis

  2. Statement of Dilemma.Note: Algebra 2 Solution #22 page 167 • As office manager, your boss has put you in charge of ordering new filing cabinets for the office. You can choose between A or B or buy a combination of A and B. • You would like to have the most storage the office can hold ( 60 sq. ft of floor space) • You would not like to exceed the budgeted amount for the cabinets.( $600) file cabinets B. Davis MathScience Innovation Center

  3. Cabinets A and B • A • requires 3 sq ft of space • can store 12 cu. Ft • costs $75 • B • requires 6 sq ft of space • can store 18 cu ft • costs $50 www.state.ok.us/ ~osi/2files.htm file cabinets B. Davis MathScience Innovation Center

  4. www.udc-office.co.jp/hud-officeE/ office1e.jpg Floor space • The office only has 60 sq ft of space: • this is a limited resource or constraint: • so…. • 3 a + 6 b < 60 b Also.. a> 0 and b > 0 a file cabinets B. Davis MathScience Innovation Center

  5. Budget • The budget is also a constraint or limitation • so… 75a +50 b < 600 www.ibrium.se/desktop_picts/ jpg/Cash(1280x960).jpg b Now the feasible region is a quadrilateral. a file cabinets B. Davis MathScience Innovation Center

  6. Storage Capacity • The office manager wants to maximize -optimize- the storage space . • Evaluate the storage equation at all 4 corner points of the feasible region. • Storage = 12 a + 18 b file cabinets B. Davis MathScience Innovation Center www.agr.state.ga.us/html/ budget__motor_vehicles___procu.htm

  7. b a Storage Capacity • Storage = 12 a + 18 b Corner Points: (0,0) Storage = 0 (0,10) Storage = 180 (8,0) Storage = 96 (2,9) Storage = 186 file cabinets B. Davis MathScience Innovation Center

  8. b a Storage Capacity • Storage = 12 a + 18 b Corner Points: (0,0) Storage = 0 (0,10) Storage = 180 (8,0) Storage = 96 (2,9) Storage = 186 Optimal solution is (2,9) file cabinets B. Davis MathScience Innovation Center

  9. Conclusion • To Optimize storage space (186 cu ft) • The office manager should spend $600 and buy 2 file A and 9 file B cabinets. A b b b b b b b b b A file cabinets B. Davis MathScience Innovation Center

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