If n maasai graze their cattle on the pasture

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During the rainy season, the Maasai of sub-Saharan East Africa are all able to graze their cattle on certain pastures. Assume that each Maasai has one cow, and wishes to fatten the cow by obtaining as much grass for that cow as possible. If N Maasai graze their cattle on a speci?c pasture the value in pounds of the total amount of grass consumed in terms of weight gain for the cattle is Q = 4N(50-N). Each cow consumes Q N . Assume a cow can be sold for $5 per pound, and that the opportunity cost of taking a cow to this pasture for each Maasai is $200.

(a) If N Maasai graze their cattle on the pasture, how much pro?t does each Maasai make?

(b) If N Maasai graze their cattle on the pasture, what is the average weight gain per cow?

(c) How many Maasai will choose to graze their cattle on the pasture?

(d) How many Maasai should graze their cattle on the pasture in order to maximize their joint pro?t?

Reference no: EM132422705

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