(50 p.) ABC Ltd buys 15 used trucks at each of two truck auctions each week held at different locations. It then transpo

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(50 p.) ABC Ltd buys 15 used trucks at each of two truck
auctions each week held at different locations. It then transports
the trucks to repair shops it contracts with. When they are
restored to ABC’s specifications, ABC sells 10 each to three
different used truck lots. There are various costs associated with
the average purchase and transportation prices from each auction to
each repair shop. Also there are transportation costs from the
repair shops to the used truck lots. ABC is concerned with
minimizing its total cost given the costs in the table
below.
a. (5 p.) Given the costs below, draw a network
representation for this problem (show all the data).
​
Repair Shops
Used Truck Lots
S1
S2
L1
L2
L3
Auction 1
550
500
S1
250
300
500
Auction 2
600
450
S2
350
650
450
b. Formulate this problem as a linear programming
model.
(5 p.) Define the decision variables
(5 p.) Formulate the objective function
(10 p.) Formulate the constraints
c. Use Excel’s Solver to find the optimal solution to
this problem.
(5 p.) Report the total cost
(20 p.) Interpret the optimal solution: how many trucks
(if any) should be sent from each Auction to each Repair Shop and
from Each Repair Shop to each Used Truck Lot?