Paul needs to construct two corrals for his pigs and his cows. The animals will be allowed to drink from the river so no fence is needed along the river. Paul has 97 feet of fence to complete the project. What should the dimensions of each corral be in order maximize the total enclosed area in the two corrals.
[ ________________l R l
[ l Pigs l i l
Y -[ --------------l v l
[ l Cows l e l
[ --------------l r l
X
a) Identify the restriction and the objective functions

Question

Paul needs to construct two corrals for his pigs and his cows. The animals will be allowed to drink from the river so no fence is needed along the river. Paul has 97 feet of fence to complete the project. What should the dimensions of each corral be in order maximize the total enclosed area in the two corrals.
     [ ________________l       R   l
     [ l     Pigs            l         i    l
Y -[ --------------l       v    l
     [ l     Cows         l          e   l
     [ --------------l        r  l
                X
a) Identify the restriction and the objective functions

anonymous · Answer

b) Use your functions from (a) above, to write the area of the corrals as a function of the
width x
A(x) =

anonymous · Answer

We know 3X + Y = 97

anonymous · Answer

Y = 97 - 3X
substitute in for Area(x) = X*Y
= X(97-3X)
97X-3X^2

anonymous · Answer

Is that right?