Diet Problem. An MIT graduate student was trying to make ends meet on a very small stipend. He went to the library and looked up the National Research Council$$s publication entitled $$Recommended Dietary Allowances$$ and was able to determine a minimum daily intake quantity of each essential nutrient for a male in his weight and age category. Let m denote the number of nutrients that he identified as important to his diet, and let bi for i $=1,2,...,$m denote his personal minimum daily requirements. Next, he made a list of his favorite foods $($which$,$ except for pizza and due mostly to laziness and ineptitude in the kitchen, consisted almost $785.$ DUALITY THEORY entirely of frozen prepared meals$).$ He then went to the local grocery store and made a list of the unit price for each of his favorite foods. Let us denote these prices as cj for j $=1,2,...,$n$.$ In addition to prices, he also looked at the labels and collected information about how much of the critical nutrients are contained in one serving of each food. Let us denote by aij the amount of nutrient i contained in food j$.($Fortunately$,$ he was able to call his favorite pizza delivery service and get similar information from them.$)$ In terms of this information, he formulated the following linear programming problem: minimize n j$=1$ cjxj subject to n j$=1$ aijxj $$ bi i $=1,2,...,$m xj $0$ j $=1,2,...,$ n$.$ Formulate the dual to this linear program. Can you introduce another person into the above story whose problem would naturally be to solve the dual?