Communication 12
To counter the increased costs of peak production, we have been working with customers on a scheme where they will commit to reduce their demand by 10% for one time period each day. We can specify the time periods when this will happen for each node but no more than 9 nodes can be reduced during the same time period.
Please provide us with the optimal total cost over the day for meeting the demand in each of the six time periods from our combined generators. We again realise that this may affect your earlier proposals on which transmission lines to upgrade and where we should build the new gas generator and solar farm.
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Communication 14
It turns out that our initial forecasts for June were rather limited. Each day there is in fact a 40% chance that demand will be higher than normal, as follows:
52, 60, 58, 62, 56, 44, 56, 57, 71, 68, 48, 51, 60, 49, 53, 67, 75, 72, 67, 59, 61, 66, 46, 54, 66, 42, 60, 37, 63, 57
The remaining 60% of the time the demand will be as previously forecast. Unfortunately, we do not know whether demand will be high or normal when we order the gas the night before.
Please provide us with the optimal expected total cost.
Communication 15
In line with the demand-reduction strategy you helped us with in Communication 12, for this new region in June we have been allocated 5 days for which we can reduce the chance of high demand from 40% to only 10% (with a 90% chance of normal demand instead). We can make this request the night before, around the same time that we order our gas. The days do not have to be consecutive. Given this opportunity, please provide us with the optimal expected total cost.
Communication 16
Our forecasters have advised us that high and normal demands tend to come in runs, so if demand is high one day, then there is actually a 50% chance it will be high again the next day, while if it is normal one day then there is only a 20% chance it will be high the next day. Requesting the next day for demand reduction will still reduce this to 10%, regardless of whether it was high or normal the previous day.
Based on this updated forecasting, please provide us with the optimal expected total cost. You can assume May 31st has normal demand.
We look forward to reading your final report.
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