A farmer raises only sheep and geese. She wants to raise at least 16 animals, including...

A farmer raises only sheep and geese. She wants to raise at least 16 animals, including 7 sheep. She spends $34 to raise a sheep and $15 to raise a goose, and she has $1020 availble for this project. Write a system of inequalities that describe all the given conditions. Graph the feasible region.

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Expert Solution

Let, the farmer raises X sheep and Y geese.

Then, (a) she wants to raise at least 16 animals, including 7 sheep.

i.e., X + Y 16.......(i) and X 7.......(ii)

(b) She spends $34 to raise a sheep and $15 to raise a goose and she has $1020 available for this project.

i.e., 34X + 15Y 1020.......(iii)

Since, the number of sheep and geese must be positive, X 0, Y 0.

Therefore, the system of inequalities is,

X + Y 16.......(i)

X 7.......(ii)

34X + 15Y 1020.......(iii)

X 0, Y 0

Here, ABCD is the feasible region.

milcah answered 1 year ago

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