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

Multiple Choice

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