Middle School Mathematical Modeling Examination Form (Open Book, Examination, Volume A)
The processing time (hours) required for the existing 9 workpieces (No A-I) and the number of workpieces to be completed in the early stage are shown in the following table.
Workpiece number A B C D E F G H I
Processing time171291551012015.
Preparatory work G, B D D D H A D F, I C
All the workpieces are processed on one machine tool. Due to machine tool failure, it is only 40 hours before all the workpieces are processed according to the agreement. According to the agreement, if each work is delayed 1 hour than planned, a penalty of 10 yuan will be paid.
(1) Please arrange a reasonable processing sequence to minimize the incidental liquidated damages; List the processing sequence you arranged and calculate the total amount of liquidated damages.
(2) What if the processing starts 50 hours before all the workpieces are processed according to the agreement?
Examination form (open book, examination, volume B)
In 20 10, southwest China was hit by a once-in-a-century drought with serious economic losses. If we can strengthen the analysis and monitoring of the current situation of drought and predict the development trend of drought in time, it will play a positive guiding role in agricultural production, drought resistance of water conservancy projects and artificial precipitation enhancement, thus ensuring local economic and social benefits. Please solve the following problems according to the above actual situation.
(1) Establish a corresponding mathematical model to simulate and forecast, and put forward a plan to suppress drought. It is suggested that the water shortage of rice can be reflected by describing the mutual transformation of precipitation, soil water, artificial irrigation water and groundwater and their interaction with farmland evaporation, and the drought index can be calculated to determine the drought level, provide drought information and provide basis for drought planning, monitoring and forecasting.
(2) Combining with their own basic education work, according to their actual units and posts, put forward a set of targeted measures that they should take.