A Mountain Village Owns a Common Pasture Where Villagers Graze

A mountain village owns a common pasture where villagers graze their goats. The cost to a goat owner of owning and caring for a goat is 4 groschens. The pasture gets overgrazed if too many goats share the pasture. The total revenue from all goats on the common pasture is f(g) = 48g - 2g², where g is the number of goats on the pasture. The town council notices that total profit from the pasture is not maximized if villagers are allowed to pasture goats for free. The council decides to allow a goat to use the common pasture only if its owner buys it a goat license. To maximize total profit (of villagers and council) , how many groschens per goat should the council charge?

A) 12
B) 20
C) 24
D) 26
E) 22

Correct Answer:

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