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 10 per foot.To separate the corrals,a fence that costs 8 per foot will divide the region.The total area of the two corrals is to be 7,000 square feet.Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing.
A) dimensions: 50 feet by 70 feet
B) dimensions: 140 feet by 50 feet
C) dimensions: 25 feet by 70 feet
D) dimensions: 35 feet by 50 feet
E) dimensions: 25 feet by 35 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 10 per foot.To separate the corrals,a fence that costs 8 per foot will divide the region.The total area of the two corrals is to be 7,000 square feet.Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing. ​  ​
A) dimensions: 50 feet by 70 feet 
B) dimensions: 140 feet by 50 feet 
C) dimensions: 25 feet by 70 feet 
D) dimensions: 35 feet by 50 feet 
E) dimensions: 25 feet by 35 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 10 per foot.To separate the corrals,a fence that costs 8 per foot will divide the region.The total area of the two corrals is to be 7,000 square feet.Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing. ​  ​
A) dimensions: 50 feet by 70 feet 
B) dimensions: 140 feet by 50 feet 
C) dimensions: 25 feet by 70 feet 
D) dimensions: 35 feet by 50 feet 
E) dimensions: 25 feet by 35 feet

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