Profit of a commodity × sales volume = total profit × unit price = sales volume.
1. A store bought a commodity and bought it in 30 yuan. During the trial sale, it is found that the daily sales volume P (pieces) of this commodity meets the relationship with the sales price X (yuan) of each piece: P= 100-2X sales volume P. If the store sells this commodity every day to make a profit in 200 yuan, what should the price of each piece be? How many pieces of this commodity are sold every day?
2. A toy factory plans to produce a toy panda, with a maximum output of 40 pandas a day, and all the products produced every day are sold. It is known that the cost of producing panda X is R (yuan) and the price is P (yuan), and the relationship between R P and X is R=500+30X, P = 170-2x respectively.
When the daily output is (1), what is the daily profit of 1750 yuan?
(2) If the maximum profit is 1950 yuan, what should be the daily output?
3. A fruit wholesale mall sells a high-grade fruit. Profit per kilogram 10 yuan, you can sell 500 kilograms every day. According to market research, if the price per kilogram increases by 1 yuan, the daily sales will be reduced by 20 kilograms. At present, commodities should ensure a daily profit of 6000 yuan, and at the same time make customers get benefits, so how much is the price increase per kilogram?
4. In the sales of clothing cabinets, it is found that a certain brand of children's clothing can sell an average of 20 pieces every day, and each piece is profitable in 40 yuan. In order to welcome Children's Day on June 1st, the shopping mall decided to take appropriate measures to reduce prices, expand sales, increase profits and reduce inventory. According to the market research, if the price of each piece of children's clothing is reduced by 4 yuan, on average, eight more pieces can be sold every day. If you want to make an average profit 1200 yuan by selling this kind of children's clothing every day, how much will the price of each child's clothing be reduced?
5. Watermelon business owners buy a batch of small watermelons at the price of 2 yuan/Jin and sell them at the price of 3 yuan/Jin, which can sell 200 Jin every day. In order to promote sales, the business owner decided to reduce the price. According to the survey, every time the price of this small watermelon is reduced by 0. 1 yuan/kg, it can sell 40 kg more every day. In addition, the daily rent and other fixed costs ***24 yuan. If business owners want to make a profit in 200 yuan every day, how much will the price of small watermelons be reduced per catty?