Answer :
Final answer:
To minimize energy expenditure, only Smelter Operation Optimization B should be operated for 15 hours, as it alone can fulfill the 30,000 tons iron ore processing requirement within the 24-hour operating limit.
Explanation:
The problem involves finding the most energy-efficient way for the smelters to operate to process at least 30,000 tons of iron ore. Since Smelter B is more efficient (it processes 2000 tons per hour while consuming only 13 megawatts compared to Smelter A's 7 megawatts for only 1000 tons per hour), we would prioritize running Smelter B where possible.
To meet the minimum requirement of processing 30,000 tons of iron ore, Smelter B would run for 15 hours (since 2000 tons/hour * 15 hours = 30,000 tons) leaving us with 9 hours for Smelter A to operate if needed without exceeding the 24-hour limit. Since Smelter B can handle the entire requirement by itself, there is no need to run Smelter A in this case.
However, if there was a situation where Smelter B couldn't handle the entire workload, the remaining load could be accommodated by Smelter A by calculating the remaining tons divided by Smelter A's efficiency (in tons/hour).
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