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

2. file cabinets B. Davis MathScience Innovation Center Statement of Dilemma. Note: Algebra 2 Solution #22 page 167 4 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. 4 You would like to have the most storage the office can hold ( 60 sq. ft of floor space) 4 You would not like to exceed the budgeted amount for the cabinets.( $600)

3. file cabinets B. Davis MathScience Innovation Center Cabinets A and B 4 A –requires 3 sq ft of space –can store 12 cu. Ft –costs $75 4 B –requires 6 sq ft of space –can store 18 cu ft –costs $50 www.state.ok.us/ ~osi/2files.htm

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

5. file cabinets B. Davis MathScience Innovation Center Budget 4 The budget is also a constraint or limitation 4 so… 75a +50 b < 600 Now the feasible region is a quadrilateral. a b www.ibrium.se/desktop_picts/ jpg/Cash(1280x960).jpg

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

7. file cabinets B. Davis MathScience Innovation Center Storage Capacity 4 Storage = 12 a + 18 b a b Corner Points: (0,0) Storage = 0 (0,10) Storage = 180 (8,0) Storage = 96 (2,9) Storage = 186

8. file cabinets B. Davis MathScience Innovation Center Storage Capacity 4 Storage = 12 a + 18 b a b Corner Points: (0,0) Storage = 0 (0,10) Storage = 180 (8,0) Storage = 96 (2,9) Storage = 186 Optimal solution is (2,9)

9. file cabinets B. Davis MathScience Innovation Center Conclusion 4 To Optimize storage space (186 cu ft) 4 The office manager should spend $600 and buy 2 file A and 9 file B cabinets. A A b b b b bbb bb