Suppose the only foods in the world are the following:
The last row imposes variety in our meals by having a limit on the number of servings/day for each of the six food types. If a satisfactory diet has to have at least 2000 kcal of energy, 55 g of protein, and 800 mg of calcium, formulate a LP model to find the least cost satisfactory diet.
Let $x_1$ be oatmeal, $x_2$ be chicken, $x_3$ be eggs, $x_4$ be whole milk, $x_5$ be cherry pie, and $x_6$ be pork and beans.
We know from the last column of the table that $$x_1\le 4,x_2\le 3,x_3\le 2,x_4\le 8,x_5\le 2,x_6\le 2$$
Satisfactory diet should be greater than or equal to 2,000 kcal of energy: $$110x_1+205x_2+160x_3+160x_4+420x_5+260x_6 \ge 2000$$
Protein should be greater than or equal to 55g $$4x_1+32x_2+13x_3+8x_4+4x_5+14x_6 \ge 55$$
Calcium should be greater than or equal to 800 mg $$2x_1+12x_2+54x_3+285x_4+22x_5+80x_6 \ge 800$$
