Mathematical modeling problem

mathematical modeling problem b-design of running time of sanitary ware

China is a country with relatively poor fresh water resources, and the per capita available fresh water is less than a quarter of the world average. Especially in recent years, due to the decrease of precipitation caused by environmental pollution, many provinces and cities have experienced large-scale drought. In order to save energy, many cities have adopted ways of raising water prices and electricity prices to curb energy consumption. On the other hand, according to relevant data, the energy consumption (mainly water consumption) of various sanitary wares produced in China is more than 6% higher than that of similar products in other developed countries.

A sanitary ware manufacturer intends to develop a fully automatic sanitary ware for men, and its water flow per unit time is constant V. In order to achieve the purpose of energy saving, there are two design schemes for controlling water discharge time.

scheme 1: when the user starts to use the sanitary ware, the sensed sanitary ware starts to discharge water with uniform water flow for a duration of t, and then automatically stops discharging water. If the use time does not exceed T-5 seconds, the water will only be drained once, otherwise, in order to keep clean, the water will be drained again after the user leaves for 1 seconds.

scheme 2: when the user starts to use the sanitary ware, the sensed sanitary ware starts to discharge water with uniform water flow for a duration of t, and then automatically stops discharging water. If the service time does not exceed T-5 seconds, the water will only be drained once, otherwise, in order to keep clean, the second water drain will be started at 2T, and the duration is also t.. However, if the service time exceeds 2t-5s, the water will be drained for the third time at 4T, and the duration is also t … In the design, in order to prolong the service life of sanitary ware as much as possible, it is generally hoped that the water will be drained for no more than 2 times for each user.

The manufacturer randomly investigated the time (unit: seconds) of 1 men from starting to leaving the sanitary ware, as shown in the following table:

Time (seconds) 12 13 14 15 16 17 18

Man-time 1 5 12 6 13 6 3

(1) Please compare the two design schemes according to the above data, which one is from the point of view of energy saving? And provide the optimal value of design parameter T (second) for the manufacturer, so that this sanitary ware can achieve the purpose of saving water and electricity to the maximum extent under the corresponding design scheme;

(2) From the point of keeping clean and saving energy, can you come up with a better design scheme? Please compare it with the previous scheme by establishing a mathematical model.

In fact, other domestic water in the family can also be used to flush the toilet. For example, after the last rinse, the clothes are cleaned, and the water discharged from the washing machine looks relatively clean. It is a pity that it flows directly into the sewer pipe. There is also water like washing face and vegetables, and it would be nice if it could be reused. Wu Hanping, an amateur inventor, developed a set of domestic water reuse device and obtained a national patent. He connected the sink in the kitchen, the basin in the bathroom and the water tank in the toilet to a water storage tank. Clean water from the sink and basin enters the water storage tank for toilet flushing.

Now I'll teach you the secret of saving water. 1. To use a water-saving toilet, add a 2-stage flushing accessory to the normal toilet. 2. The floating cake under the water tank is removed to form the stepless controlled water outlet.

3. The flushing time of urinal automatic flusher is shortened. 4. Water the flowers, wash the car and scrub the floor with clear water such as rice water, laundry water, dish washing water and bath water. 5. The carpet cleaning method is changed from wet or steam to dry powder. 6. Recover and reuse the water collected by dehumidifier and the wastewater from water purification equipment such as pure water machine and distilled water machine.

now that I've finished the six water-saving secrets, do you think of a better way to save water than me? Are you saving water? I think you should be saving water!

For a long time, people generally think that water is "inexhaustible", and they don't know how to cherish it, but waste it. In fact, water resources are increasingly scarce, and the urban water supply work in our city is struggling on the edge of serious water shortage, and tap water is hard to come by.

People can't live without water for a day. Water is the source of life. Cherishing water means cherishing your own life! Here, we introduce some water-saving common sense in daily life:

Brush your teeth

Waste: continuously drain water for 3 seconds, and use about 6 liters of water.

water saving: cups are connected with water, and 3 cups use .6 liters of water. A family of three can save 486 liters of water twice a day.

Laundry

Waste: The washing machine washes and drains water continuously while filling water, which requires about 165 liters of water each time.

water saving: the washing machine is washed by washing-dehydration-water injection-dehydration-water injection-dehydration, and 11 liters of water is used each time, saving 55 liters of water each time, and washing four times a month can save 22 liters of water.

In addition, centralized laundry can reduce the number of laundry; Hand washing is advocated for small pieces and a small amount of clothes, which can save a lot of water; Too much detergent will waste a lot of water.

bathing

waste: a lot of water will be wasted if the water is continuously showered for a long time.

Too much water is spilled in the bath, or when the water plug is opened and water is injected in the bath, the waste will be amazing.

water saving: intermittent water shower (such as pedal, induction, etc.). Turn off the water in time when scrubbing. Avoid showering for too long.

The water after bath can be used for washing clothes, washing cars, flushing toilets and mopping floors.

Cooking

Waste: leave the faucet open and rinse for a long time. Boiling water for too long, a lot of water vapor evaporates. Rinse vegetables and fruits with tap water.

water-saving: the oil stain on the cookware can be wiped off with paper first, and then washed, which can save water.

control the flow of the faucet, and change the continuous flushing to intermittent flushing.

car washing

waste: rinse with water pipe for 2 minutes, using about 24 liters of water.

water saving: it takes 3 buckets of water to wash the car, and the water consumption is about 3 liters. Use washing water and washing water to wash the car. Rinse with water-saving spray gun. Use mechanical automatic car washing, car washing water treatment recycling.

Water-saving tips:

Saving water is beneficial to the present age, and it will make a great contribution to the future generations. This is how the students worked out some water-saving tips for life after discussion:

First, washing vegetables with rice water and then washing them with clear water not only saves water, but also effectively removes the residual pesticides on vegetables;

second, wash the mop, sweep the floor and then flush the toilet. The second washing water for washing clothes cleans doors and windows, furniture, shoes and socks, etc.

thirdly, flush the toilet after urinating and urinating, and try not to turn on the big water pipe for flushing, but make full use of the used "dirty water";

4. Sprinkle water on indoor and outdoor floors to cool down in summer, and try not to use clean water, but use laundry water after laundry;

5. When cleaning bicycles and family cars, use a wet cloth instead of water. In places that are too dirty, it is also advisable to use the remaining water after washing clothes.

VI. Flushing toilets: If you use water-saving equipment, you can save 4-5 kg of water each time;

7. Watering flowers at home should use rice washing water, tea, laundry water, etc.

8. Wash towels, small objects, fruits and other small amounts of water at home. It is advisable to use a basin to hold water instead of turning on the tap to flush it;

9. floor washing: scrubbing with a mop can save more than 2kg of water for each household than washing with a faucet;

1. If the faucet leaks after being used for a long time, you can cut the rubber cover of the small penicillin bottle and put it in, which can ensure that it is watertight;

Xi. Adjust the floating ball of the water tank in the bathroom down by 2 cm, which can save nearly 3 kg of water each time; If you use it four times a day at home, you can save 438kg of medicine a year.

12. Vegetable washing: wash one basin at a time, and don't run the faucet, which can save 5kg; for one meal;

XIII. Shower: If you turn off the tap and wipe the soap, you can save 6kg; of water by taking a shower;

XIV. Washing clothes by hand: If you wash and clean clothes in a washbasin, you will save 2kg; of water each time compared with running the tap;

XV. Washing clothes with a washing machine: It is recommended that you fill a bucket before washing. If you wash it twice separately, it will consume 12kg; more water.

XVI. Car washing: Washing with a rag can save at least 4kg; of water each time compared with washing with a faucet;