Suppose there are the following one-way shipping lanes from the following cities to the following cities, with the specified maximum capacities of tons of tomatoes per year: From To Capacity
Athens Baltimore 5:1
Athens Cairo 7:2
Cairo Baltimore 2:1
Baltimore Delhi 5:9
Cairo El Paso 3:1
Delhi El Paso 2:9
Delhi Frankfurt 4:0
El Paso Franfurt 10:5

Consider the problem of nding how many tons of (nonperishable) tomatoes should be sent yearly along each of these dierent shipping lanes to maximize the the number of tomatoes delivered from Athens to Frankfurt (assuming that tomatoes are grown in Athens and eaten in Frankfurt, and are neither created nor destroyed in any of the other cities). Express this problem as a linear programming problem in standard form. For a little extra credit, find a solution to this problem in an ad-hoc way, but Demonstrate that your solution is indeed optimal.