1 2 we will multiply equation 1 by 2 and equation 2

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(1) (2) We will multiply equation (1) by 2 and equation (2) by –3 to obtain the following: (1) (2) Adding the above two equations, gives us Substituting F =60 in equation (1), gives us the following: Therefore, the point of intersection G is (40, 60). We now have all the corner points of the feasible region. Step 4: Test the corner points to determine the optimal solution Corner point Total profit O (0, 0) 0 D (70, 0) 1750 G (40, 60) 1900 C (0, 120) 1800 Therefore, the optimal solution is as follows: Number of Air-conditioners = 40 Number of Fans = 60 Total Profit = $1900 3
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QSO 510 Quantitative Analysis Linear Programming Review Problems Solutions c) Excel Solver Here is how the spreadsheet was set up for Excel Solver. The spreadsheet shows 10 for air- conditioners and 10 for fans. These numbers were selected arbitrarily. Any quantities can be entered for air-conditioners and fans since Excel Solver would find the optimal solution anyway. Electrocom p Corporatio n Variables Air Conditioners Fans Quantity 40 60 Objective Air Conditioners Fans Total Profit Unit Profit $25 $15 $1,900 Constraints Baseballs Softballs Total Limits Wiring Hours 3 2 240 < = 240 Drilling Hours 2 1 140 < = 140 Excel Solver produced the following Answer Report: Objective Cell (Max) Cell Name Original Value Final Value $D$7 Unit Profit Total Profit $1,900 $1,900 Variable Cells Cell Name Original Value Final Value Integer $B$4 Quantity Air Conditioners 40 40 Contin $C$4 Quantity Fans 60 60 Contin Constraints Cell Name Cell Value Formula Status Slack $D$10 Wiring Hours Total 240 $D$10<=$F$10 Binding 0 $D$11 Drilling Hours Total 140 $D$11<=$F$11 Binding 0 From the answer report, we can read the optimal solution as follows: Number of Air-conditioners = 40 4
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QSO 510 Quantitative Analysis Linear Programming Review Problems Solutions Number of Fans = 60 Total Profit = $1,900 5
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QSO 510 Quantitative Analysis Linear Programming Review Problems Solutions Review Problem 2 George Rifkin is considering investing some or all of a $60,000 inheritance in a one-year certificate of deposit paying a fixed 6% or a venture capital group project with a guaranteed 3% return but the potential of earning 10%. George would like to invest the minimum amount necessary to achieve a potential return of at least $4000 and a guaranteed return of at least $2000. a) Formulate a mathematical model so that George can keep as much money as possible for himself and still meet his investment criteria? b) Use the corner point graphical approach to solve the model you formulated. c) Use Excel Solver to solve the model you formulated. (Lawrence and Pasternack, Applied Management Science, Second Edition, 2002, Page 105) Solution a) Formulate the Linear Programming Model Step 1: Define variables C = Dollar investment in certificate of deposit V = Dollar investment in venture capital Step 2: Write objective function Minimize total investment Step 3: Write constraints Guaranteed return: (1) Potential return: (2) Total investment: (3) Non-negativity: , b) The Graphical Method Step 1: Plot the constraints The non-negativity constraints require that we stay within the first quadrant. Therefore, all constraints would be drawn in the first quadrant.
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