A Zoo Is Designing a Giant Bird Cage Consisting of a Cylinder

Essay

A zoo is designing a giant bird cage consisting of a cylinder of radius r feet and height h feet with a hemisphere on top (no bottom).The material for the hemisphere costs $20 per square foot and the material for the cylindrical sides costs $10 per square foot; the zoo has a budget of $5120.Find the values of r and h giving the birds the greatest space inside assuming the zoo stays within its budget.