Final answer:
In a transportation problem with four sources and three destinations, there are seven supply and demand constraints (one for each source and destination), plus 12 non-negativity constraints for the routes, totaling 19 constraints in the LP model.
Step-by-step explanation:
In a typical transportation problem with four sources and three destinations, the number of constraints for the Linear Programming (LP) model can be determined by considering the supply constraints for each source and the demand constraints for each destination. There will be one supply constraint for each source and one demand constraint for each destination.
Therefore, with four sources, we have four supply constraints, and with three destinations, we have three demand constraints. Adding these together gives us a total of seven constraints. However, if we include the non-negativity constraints, which dictate that the number of goods transported must be non-negative, the total number of constraints will be the number of routes between sources and destinations, which is 4 times 3, giving us 12 non-negativity constraints.
So, the total number of constraints will be the sum of the supply, demand, and non-negativity constraints, which is 7 supply and demand constraints plus 12 non-negativity constraints, resulting in 19 constraints altogether for this LP model.