Utility maximization problem

In microeconomics, the utility maximization problem is the problem consumers face: 'how should I spend my money in order to maximize my utility?' It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending as well as the prices of the goods. In microeconomics, the utility maximization problem is the problem consumers face: 'how should I spend my money in order to maximize my utility?' It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending as well as the prices of the goods. Suppose the consumer's consumption set, or the enumeration of all possible consumption bundles that could be selected if there were no budget constraint, has L commodities and is limited to positive amounts of consumption of each commodity. Let x be the vector x={xi;i=1,...L} containing the amounts of each commodity; then Suppose also that the price vector (p) of the L commodities is positive, and that the consumer's income is I {displaystyle I} ; then the set of all affordable packages, the budget set, is where ⟨ p , x ⟩ {displaystyle langle p,x angle } is the dot product of p and x, or the total cost of consuming x of the products at price level p: