$31.$A new airport being built will have three terminals and two baggage pickup areas.

An automated baggage delivery system has been designed to transport the baggage

from each terminal to the two baggage pickup areas. This system is depicted

graphically in Figure $5\mathrm{.}43,$ where nodes $1,2,$ and $3$ represent the terminals, and

nodes $7$ and $8$ represent the baggage pickup areas. The maximum number of bags

per minute that can be handled by each part of the system is indicated by the value

on each arc in the network.a$.$ Formulate an LP model to determine the maximum number of bags per minute that can be delivered by this system.

b$.$ Use Solver to find the optimal solution to this problem. spreadsheet solution please solved in excel