10. A hotel has 100 standard rooms, with a room rate of 400 yuan/day, but the occupancy rate is only $50 \%$. If the room rate is reduced by 20 yuan, it can increase the number of occupied rooms by 5. Find the appropriate room rate to maximize the hotel's room revenue,


【Answer】 22500
【Analysis】The initial situation is: 400 yuan, 50 rooms. Let the price be reduced by $x$ times 20 yuan,
The room fee is: $(400-20 x)(50+5 x)=100(20-x)(10+x)$
And $(20-x)+(10+x)=30$, the sum is constant, the product is maximized when the difference is minimized, $20-x=10+x=15$ at the maximum;
So the highest room fee at this time is: $100 \times 15 \times 15=22500$ (yuan).