Wonka Widget, Inc. faces a three-period inventory model. The manufacturing cost per widget varies from period to period. These costs are $2, $4, and $3 for periods, 1, 2, and 3, respectively. A cost of $1 is incurred for each unit of inventory that is carried from one period to the next. Demand is 10,000, 20,000, and 30,000 units in periods 1, 2, and 3, respectively. The initial and final inventories are zero. Formulate an LP to determine how much the manufacturer should produce during each period to satisfy demand at minimum cost.