Wine in Your Knapsack?

We pose three Knapsack Problems (KPs) to select the rank-maximizing subset of wines subject to budget and quantity constraints. The first problem seeks the subset of wines, from a single cultivar (zinfandel) that maximizes the sum of rank subject to a budget constraint. We modify this problem by adding an equality constraint on the number of bottles that must be chosen. The third problem seeks to maximize the sum of ranks from three different cultivars (cabernet sauvignon, pinot noir, and zinfandel) subject to a budget constraint and then a budget and minimum bottle constraints for each cultivar. The sum of rank maximization problems may have multiple solutions. We also pose two expenditure minimization problems, subject to achieving the maximum sum of ranks. We also explore how a KP might be formulated when wine is viewed as an investment.