Denver Transportation Company is considering investing in several projects that have varying capital requirements over the next four years. Faced with limited capital each year, management would like to select the most profitable projects that it can afford. The estimated net present value for each project, the capital requirements, and the available capital over the four-year period are shown in the following binary integer linear programming model.  

?
Questions
1. What is the optimal solution?
2. What is the total estimated net present value at the optimal solution?
3. Based upon the optimal solution and slack variables, what recommendations could you make to management?
?
WhereS = 1 if the store expansion project is accepted; 0 if rejectedF = 1 if the fleet expansion project is accepted; 0 if rejectedM= 1 if the equipment upgrade project is accepted; 0 if rejectedR= 1 if the market research project is accepted; 0 if rejectedand currency is in $1,000s.Maximize75S + 50F + 16E + 12Rs.t.30S + 30F + 10E + 20R ? 8530S + 35F + 20E + 10R? 6040S + 50F + 20E + 10R? 10065S + 55F + 20E + 10R? 125S, F, E, R = 0, 1 (binary)?

What will be an ideal response?

 ModelSFERMax NetPresent Value
 Store ExpansionFleet ExpansionEquipment Upgrade
Market Research
 
Objective Function
 1011 
Coefficients $75$50$16$12
$103
Max Net Present Value: =SUMPRODUCT(F7:I7, $F$6:$I$6)S = 0, F = 1, E = 1, and R = 1. So, management should invest in the store expansion, equipment upgrade, and market research, which will generate a maximum present net value of $103,000. There will be $15,000 in Year 1, $30,000 in Year 3, and $30,000 in Year 4; therefore, it is possible to accumulate the four-year total slack of $75,000 to fund Fleet Expansion. An added $35,000 would yield a return of an additional $153,000.?
 ConstraintsResources Used  Available
Year 1 Capital$30
 $30 $10$20   $60 ? $85
Year 2 Capital$30
 $35 $10 $10 $60 ? $60
Year 3 Capital$40
 $50 $20 $10 $70 ? $100
Year 4 Capital$65 $55$20   $10 $95 ? $125
?$60 = =SUMPRODUCT(F11:I11,$F$6:$I$6)$60 = =SUMPRODUCT(F12:I12,$F$6:$I$6)$70 = =SUMPRODUCT(F13:I13,$F$6:$I$6)$95 = =SUMPRODUCT(F14:I14,$F$6:$I$6)??

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