The management scientist entered a trance-like state as he formulated his model. This state was interrupted by an integer-hating colleague,
who insisted that the model should be run as a linear program rather than integer program. The management scientist sighed, relaxed the integer constraint, and ran the model, obtaining the following answer report. Provide a full interpretation and plan for action.
Variable Cells
Cell Name Original Value Final Value Integer
$G$4 wood floors Contractor? 0 0 Contin
$H$4 wood floors Landlord? 0 1 Contin
$G$5 kitchen tile Contractor? 0 0.833 Contin
$H$5 kitchen tile Landlord? 0 0.167 Contin
$G$6 back door Contractor? 0 0.000 Contin
$H$6 back door Landlord? 0 0 Contin
$G$7 garage door opener Contractor? 0 1 Contin
$H$7 garage door opener Landlord? 0 0 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$B$12 Total Time Weeks Contractor 4 $B$12<=$B$13 Binding 0
$E$10 Total Cost Contractor Price $3,000 $E$10<=$E$11 Binding 0
$I$4 wood floors Included? 1 $I$4<=$J$4 Binding 0
$I$5 kitchen tile Included? 1 $I$5<=$J$5 Binding 0
$I$6 back door Included? 2.78E-16 $I$6<=$J$6 Not Binding 1
$I$7 garage door opener Included? 1 $I$7<=$J$7 Binding 0
Answer: The landlord uses the entire budget, takes the entire four weeks and installs (or has the contractor install) the floors, garage door, and the kitchen tile, leaving only the back door off the improvement list. The kitchen tile project is split between the landlord, who does one-sixth of the work, and the contractor, who completes the remaining five-sixths. Although the model meets the constraints, this is not a practical solution in the real world. The management scientist should realize that moving to an integer solution within the LP feasible region will result in a feasible solution, albeit one with no guarantee of optimality. If the integer solution of wood floors and the garage door is chosen, there would be money and time both left over in the project budget, but the management scientist should reintroduce the integer constraint to confirm the best choice of action.