40 Problem 2: (Multi-Period Production Planning) Steel is made from iron, and iron ore is the primary raw material for steel production. (Iron ore is the rocks and minerals from which metal iron is extracted.) One needs 1.5 tons of iron ore in order to produce 1 ton of steel. AUH Steel Co. needs to make its steel production plan for the four quarters of 2018. The following table shows the demand, unit production cost, inventory carrying cost rate of steel for these four quarters. The same table also provides amount of iron ore that the company will purchase in each quarter. Quarter ! Quarter 2 Quarter 3 Quarter 4 Demand (tons) 450,000 220,000 300,000 290,000 Production Cost (S/ton) 650 850 500 700 Inventory Cost ($/ton/quarter) 32 27 36 Iron Ore Purchase 700,000 500,000 300,000 500,000 The company has rented a storage place to store its excess inventory. The place can take a maximum of 120,000 tons of steel. Formulate an LP to prepare a four-period production plan that will satisfy AUH Steel's demand require- ments at a minimum cost. (a) (3 points) Specify the decision variables: (6) (4 points) Write down the objective function: (c) (5 points) Write down the inventory equilibrium constraints: (d) (5 points) Write down the raw material constraints: (e) (3 points) Write down the storage constraints