A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 15 per foot. To separate the corrals, a fence that costs 6 per foot will divide the region. The total area of the two corrals is to be $6000$ square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing.
A)dimensions: $50$ feet by $60$ feet
B)dimensions: $60$ feet by $50$ feet
C)dimensions: $25$ feet by $60$ feet
D)dimensions: $30$ feet by $50$ feet
E)dimensions: $25$ feet by $30$ feet

Question

A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 15 per foot. To separate the corrals, a fence that costs 6 per foot will divide the region. The total area of the two corrals is to be $6000$ square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing. 
A)dimensions: $50$ feet by $60$ feet 
B)dimensions: $60$ feet by $50$ feet 
C)dimensions: $25$ feet by $60$ feet 
D)dimensions: $30$ feet by $50$ feet 
E)dimensions: $25$ feet by $30$ feet

Quizplus · Accepted Answer

The Answer of A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 15 per foot. To separate the corrals, a fence that costs 6 per foot will divide the region. The total area of the two corrals is to be $6000$ square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing. 
A)dimensions: $50$ feet by $60$ feet 
B)dimensions: $60$ feet by $50$ feet 
C)dimensions: $25$ feet by $60$ feet 
D)dimensions: $30$ feet by $50$ feet 
E)dimensions: $25$ feet by $30$ feet

A Rancher Plans to Use an Existing Stone Wall and the Side