EXAMPLE 1 A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x, y, and z to be the length, width, and height, respectively, of the box in meters. Then we wish to maximize V = xyz subject to the constraint g(x, y, z) = 2xz + 2yz + xy = 48. Using the method of Lagrange multipliers, we look for the values of x, y, z, and λ such that ∇V = λ∇g and g(x, y, z) = 48. This gives the equations vx = λgx vy = λgy vz = λgz 2xz + 2yz + xy = 48

(01.02 mc) asap plzzzwhich of the following correctly simplifies the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared.? select one: a. 3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 1 squared over 4 squared. = 1 over 6.b. 3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 0 over 4 squared. = 0c. 3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 0 over 4 squared. = 0d. 3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 1 squared over 4 squared. = 81 over 16.