The strategic bomber command receives instructions to intercept the enemy's tank production. The enemy has 4 key plants located in separate cities and destruction of any one plant will effectively halt the production of the tanks. There is an acute shortage of fuel which limits the supply to 48,000 gallons for this particular mission. Any bomber sent to any particular city must have at least enough fuel for the round trip plus a reserve of 100 gallons. No damage is inflicted on a plant by a bomber that fails to destroy it. Details of bombers available to the command, enemy plant locations and their destruction probabilities are given below: Bomber Type Description Miles per gallon Number available 1 Heavy 2 48 2 Medium 3 32 Plant Distance from base (Miles) Probability of destruction by Heavy bomber Medium bomber 1 450 0.10 0.08 2 480 0.20 0.16 3 540 0.25 0.20 4 600 0.25 0.20 Find how many of each type of bombers should be dispatched and to which enemy plants in order to maximize the probability of success. Formulate only.