2. {10 marks} A certain construction company requires the use of steel for the next 8...

 

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2. {10 marks} A certain construction company requires the use of steel for the next 8 months, according to the following table. Month 1 2 3 4 5 6 7 8 Steel required (tons) 50 70 80 80 30 100 110 60 Each month, there are 3 ways to order steel: Order steel that is readily available for $1,000 per ton. Order steel that will be available one month later for $900 per ton, but at most 40 tons can be ordered per month. Order steel that will be available two months later for $800 per ton, but at most 30 tons can be ordered per month. We start at month 1 with no steel. We assume that any steel ordered for the month will arrive at the beginning of the month, and is used throughout the month. Any steel that is not expected to be used for that month needs to be put in storage at the start of the month, at a cost of $50 per ton per month. The storage has a maximum capacity of 50 tons. At the end of the 8th month, no unused steel should remain. Write a linear program that satisfies all the constraints while minimizing the total cost of buying and storing steel. 2. {10 marks} A certain construction company requires the use of steel for the next 8 months, according to the following table. Month 1 2 3 4 5 6 7 8 Steel required (tons) 50 70 80 80 30 100 110 60 Each month, there are 3 ways to order steel: Order steel that is readily available for $1,000 per ton. Order steel that will be available one month later for $900 per ton, but at most 40 tons can be ordered per month. Order steel that will be available two months later for $800 per ton, but at most 30 tons can be ordered per month. We start at month 1 with no steel. We assume that any steel ordered for the month will arrive at the beginning of the month, and is used throughout the month. Any steel that is not expected to be used for that month needs to be put in storage at the start of the month, at a cost of $50 per ton per month. The storage has a maximum capacity of 50 tons. At the end of the 8th month, no unused steel should remain. Write a linear program that satisfies all the constraints while minimizing the total cost of buying and storing steel.