Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x 7y 4z

Several paint mixtures are made by mixing blue paint and white paint. paint colors blue paint white paint mixture a 5 cups 12 cups mixture b 6 cups 6 cups mixture c 4 cups 12 cups mixture d 5 cups 6 cups which mixture has the highest ratio of blue paint to white paint