The problem said:
A caterer must supply 110 napkins on Monday, 90 on Tuesday, 130 on Wednesday, and 170 on Thursday. The caterer initially has no napkins on hand. New napkins can be bought for 7 cents each. Used napkins can be laundered for use the next day at 4 cents/napkin or laundered for use in 2 days or more at 2 cents/napkin. At the end of the week, all used napkins have no value. How can the caterer meet these demands at minimal cost? (Hint> consider this as a transportation problem with four sources-the new-napkin outlet and the first 3 days' collections of used napkins.)
I try to setup the tableu but I can't apply the algoritm to find the correct distribution due, I can not be able to figure out the correct supply and demand in each extrem of the tableau.
Below, is the my tableu so far:
7 -cost of new napking 4- fast laundry 2- slow laundry
The minimal cost (show in book said): $22.4
I really apreciate any help, in set up this tablaeu.
I would try to fill in the tableau from a graphical representation of the problem:
The difficulty comes from the fact that arcs are in both directions, meaning that destination nodes are also origin nodes, and vice versa. I think the following tableau might be correct, but not 100% sure: