Current location - Training Enrollment Network - Mathematics courses - Mathematical modeling problem
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 the way of raising water 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 60% higher than that of similar products in other developed countries.

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

Scheme 1: When the user starts to use the sanitary ware, the sensed sanitary ware starts to flow out with uniform water for t, and then automatically stops flowing out. If it is used for less than T-5 seconds, it will only be drained once; otherwise, in order to keep it clean, it will be drained again after the user leaves for 10 second.

Scheme 2: When the user starts to use the sanitary ware, the sensed sanitary ware starts to flow out with uniform water for t, and then automatically stops flowing out. If the service time does not exceed T-5 seconds, the water will be drained once, otherwise, in order to keep clean, the second drainage will be started at 2T, and the duration will be t ... But if the service time exceeds 2t-5s, the third drainage will be conducted at 4T, and the duration will be t ... In the design, in order to prolong the service life of sanitary ware as much as possible, it is generally hoped that each user will drain water no more than twice.

The manufacturer randomly investigated 100 men's time (unit: seconds) from beginning to leaving the sanitary ware. Please refer to the following table:

Time (seconds)12131415161718.

Person-times1512601363

(1) Please compare the two design schemes according to the above data. Which one is better from the perspective of energy saving? And provide the optimal value of the 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 perspective of keeping clean and saving energy, can you propose a better design scheme? Please compare it with the previous scheme by establishing a mathematical model.

In fact, other domestic water can also be used to flush toilets. For example, after the last rinse, the clothes are washed clean, and the water discharged from the washing machine looks cleaner. Unfortunately, it flows directly into the sewer. There is also water such as washing your face and vegetables. 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 bathroom to a water storage tank. Clean water from the sink and basin enters the storage tank for flushing the toilet.

Now I'll teach you the secret of water saving 1. To use the water-saving toilet, please install a two-stage flushing accessory for the ordinary toilet. 2. Remove the floating cake under the water tank to form a stepless control water outlet.

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

Now that I have finished six secret recipes for water saving, have you thought of a better way to save water than me? Are you saving water? I think you should save water!

For a long time, people generally believe that water is "inexhaustible". If you don't know how to cherish it, you will 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/teeth

Waste: continuous drainage for 30 seconds, using about 6 liters of water.

Water saving: cups are connected with water, 3 cups use 0.6 liters of water. A family of three can save 486 liters of water twice a day.

wash clothes

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

Water saving: the washing machine adopts the washing-dehydration-water injection-dehydration-water injection-dehydration mode, and the water consumption is 1 10 liter each time, which can save 55 liters and 220 liters each time.

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.

have a bath

Waste: A long uninterrupted water shower will waste a lot of water.

Too much bath water, or even overflow, or open the water plug and inject water at the same time, the waste will be amazing.

Water saving: intermittent water shower (such as pedaling, induction, etc.). ). Turn off the water in time when scrubbing. Avoid taking a long shower.

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

cook

Waste: the tap was left on for a long time. Boiling water for too long, a lot of water vapor evaporates. Rinse vegetables and fruits with tap water.

Water saving: oil stains on cookware and tableware can be wiped off with paper before washing, which can save water.

Control the flow of the faucet, and change the uninterrupted flushing into intermittent flushing.

wash a car

Waste: Rinse with water pipe for 20 minutes and use about 240 liters of water.

Water saving: 3 barrels of water are needed for car washing, and the water consumption is about 30 liters. Wash the car with car wash water and car wash water. Rinse with a water-saving spray gun. Use mechanical automatic car washing, car washing water treatment recycling.

Small ways to save water:

Saving water is beneficial to the present and will make great contributions to the future. After discussion, the students came up with some ways to save water in life:

1. Washing vegetables with rice-washing water and then with clear water not only saves water, but also effectively removes pesticide residues 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.

Third, flush the toilet after urinating, try not to open the big water pipe for flushing, and make full use of the used "dirty water";

4. Sprinkle water on the indoor and outdoor ground in summer to cool down, try not to use clear water, and use washing water after washing;

5. When cleaning bicycles and family cars, don't wash them with water, but wipe them with a wet cloth. If it is too dirty, wash it with the water left over from washing clothes.

6. Flushing the toilet: If you use water-saving equipment, you can save 4-5 kilograms of water each time;

Seven, family watering flowers, appropriate use Taomi water, tea, laundry water, etc. ;

Eight, household washing towels, small objects, fruits and other small amounts of water. It is advisable to use a basin to hold water instead of turning on the tap to flush;

9. Washing the floor: scrubbing with a mop can save more than 200 kilograms of water than washing each household with a faucet;

Ten, faucet used for a long time leaks. The rubber cover of the small penicillin bottle can be cut open to ensure no water leakage;

1 1. Adjust the floating ball in the toilet water tank down by 2 cm, saving nearly 3 kg of water each time; If you use it four times a day at home, you can save 4380kg of medicine a year.

Twelve, washing vegetables: a pot of a pot, do not run the faucet, a meal can save 50kg;;

13. Shower: If you turn off the tap to wipe soap, you can save 60kg of water by taking a shower;

14. Hand-washing clothes: If you use the washbasin to wash clothes, you will save 200kg of water each time compared with turning on the tap;

15. Washing clothes with a washing machine: I suggest you fill a bucket before washing. If washed twice separately, it will consume120kg; More water.

Sixteen, car washing: scrubbing with a rag can save at least 400kg. Compared with washing with a faucet, the water consumption is much less each time;