Solve the Problem $\frac { 1 } { 4 }$ Of the Supplies Will Get Through, but 8 Army Soldiers

question 50

Multiple Choice

Solve the problem.
-A certain army is engaged in guerrilla warfare. It has two ways of getting supplies to its troops: it can send a convoy up the river road or it can send a convoy overland through the jungle. On a given day, the guerrillas can watch only one of the two roads. If the convoy goes along the river and the guerrillas are there, the convoy will have to turn back and 6 army soldiers will be lost. If the convoy goes overland and encounters the guerrillas, $\frac { 1 } { 4 }$ of the supplies will get through, but 8 army soldiers will be lost. Each day a supply convoy travels one of the roads, and if the guerrillas are watching the other road, the convoy gets through with no losses. If the army chooses the optimal strategy to maximize the amount of supplies it gets to its troops and the guerrillas choose the optimal strategy to prevent the most supplies from getting through, then what portion of the supplies will get through?

• A) \(\frac { 4 } { 11 }\)
• B) \(\frac { 3 } { 7 }\)
• C) \(\frac { 4 } { 7 }\)
• D) \(\frac { 1 } { 2 }\)

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