The Stigler Committee Report [20, 21, 22] has stressed the desirability of revising the Consumer Price Index in the direction of a fixed-utility cost-of-living index. This paper proposes that a linear programming approach might be feasible for developing the food component price index of a cost-of-living index, and perhaps also for some other components. The main advantage of the linear programming approach would be that it recognizes substitutions among goods and services as prices change, whereas the conventional fixed market-basket approach to the formulation of index numbers makes no provision for such trading off of commodities and services.