Phil Bert's Nuthouse Is Preparing a New Product, a Blend

Essay

Phil Bert's Nuthouse is preparing a new product, a blend of mixed nuts. The product must be at most 50% peanuts, must have more almonds than cashews, and must be at least 10% pecans. The blend will be sold in one-pound bags. Phil's goal is to mix the nuts in such a manner that all conditions are satisfied and the cost per bag is minimized. Peanuts cost $1 per pound. Cashews cost $3 per pound. Almonds cost $5 per pound and pecans cost $6 per pound. Identify the decision variables of this problem. Write out the objective and the set of constraints for the problem. Do not solve.