The Rent-A-Dent car rental company allows its customers to pick up a rental car at one location and return it to any of its locations. Currently, two locations (1 and 2) have 13 and 17 surplus cars, respectively, and four locations (3, 4, 5, and 6) each need 10 cars. The costs of getting the surplus cars from locations 1 and 2 to the other locations are summarized in the following table.
Costs of Transporting cars between Locations
Location 3 Location 4 Location 5 Location 6
Location 1 $54 $17 $24 $29
Location 2 $25 $18 $19 $32
Because 30 surplus cars are available at locations 1 and 2, and 40 cars are needed at locations 3, 4, 5, and 6, some locations will not receive as many cars as they need. However, management wants to make sure that all the surplus cars are sent where they are needed, and that each location needing cars receives at least five. (Let
Xij
be the number of cars sent from
Location i
to
Location j.)
(a)
Formulate an LP model for this problem to minimize cost (in dollars).
MIN:
54X13​+17X14​+24X15​+29X16​+25X23​+18X24​+19X25​+32X26​
Subject to:total location 1
X13​+X14​+X15​+X16​=13
total location 2
X23​+X24​+X25​+X26​=17
Minimum sent to Location 3
X13​+X23​≥5
Minimum sent to Location 4
X14​+X24​≥5
Minimum sent to Location 5
X15​+X25​≥5
Minimum sent to Location 6
X16​+X26​≥5
Maximum sent to Location 3
X13​+X23​≤10
Maximum sent to Location 4
X14​+X24​≤10
Maximum sent to Location 5
X15​+X25​≤10
Maximum sent to Location 6
X16​+X26​≤10
X13, X14, X15, X16, X23, X24, X25, X26 ≥ 0
(b)
Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution?
(X13, X14, X15, X16, X23, X24, X25, X26) =