Problem
A commercial food for caged reptiles is made in 40-pound bags from five potential feeds. For labeling purposes, feed A must constitute at least 20% of each bag by weight, and each of feeds B to E must be at least 5% of the total weight. Further, feeds B and D must together constitute at least 30% by weight, and feeds B, C, and E together must be no more than 50% by weight. The costs per pound for feeds A to E are, respectively, $0.96, $0.85, $0.775, $0.45, and $0.375. How shall this reptile food be made, and what is the cost per bag?