3. A cereal manufacturer wishes to produce 1000 pounds of a cereal that contains exactly 10% fiber, 2% fat, and 5% sugar (by weight). The cereal is to be produced by combining four items of raw food material in appropriate proportions. These four items are named A, B, C, D and they have certain combinations of fiber, fat, and sugar content, and are available at various prices per pound: Item A BC D % fiber 3 8 16 4 %fat 6 46 9 9 %sugar 20 5 4 0 2 Price/lb 2 4 1 The manufacturer wishes to find the amounts of each item to be used to produce the cereal in the least expensive way. Formulate the problem as a linear programming problem and convert it to the standard form.