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A fruit company uses 20 vehicles to transport 42 kinds of a, B and C fruits to other places for sale. Each vehicle can only transport the same kind of fruit, full of each kind of fruit
If M cars are arranged to carry a kind of fruit, n cars are arranged to carry B kinds of fruit, then (20-m-n) cars are arranged to carry C kinds of fruit
According to the meaning of the title, 2.2m + 2.1n + 2 (20-m-n) = 42 n = 20-2m
Let the profit of this shipment be w, then w = 6 × 2.2m + 8 × 2.1n + 5 × 2 × (20-m-n) = - 10.4m + 336
When m = 2, w = 315.2 (hundred yuan) = 31520 (yuan)
That is to say, 2 trucks were used to transport a and C kinds of fruits respectively, and 16 trucks were used to transport B kinds of fruits, which made the fruit base obtain the maximum profit of 31520 yuan
A local product company organized 20 vehicles to transport 120 tons of a, B and C local products to other places for sale. According to the plan, all 20 vehicles will be shipped, and each vehicle can only carry the same local product, and must be full. According to the information provided in the table below, the following questions will be answered: the carrying capacity (ton) of each vehicle of a, B and C local products is 8 65 Profit per ton of local products (100 yuan) 12 16 10 (1) suppose the number of vehicles carrying a local product is x, and the number of vehicles carrying B local product is y, and find the functional relationship between Y and X. (2) if the number of vehicles carrying each local product is not less than 3, then there are several arrangements for the vehicles, and write each arrangement. (3) which arrangement in (2) should be adopted to maximize the profit of this sale? And calculate the value of the maximum profit
(1) ∵ 8x + 6y + 5 (20-x-y) = 120, ∵ y = 20-3x. The functional relationship between Y and X is y = 20-3x. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (3 points) (2) from X ≥ 3, y = 20-3 x ≥ 3, that is, 20-3 x ≥ 3, from X ≥ 3, y = 20-3 x ≥ 3, that is, 20-3 x ≥ 3, we can get 3 ≤ x ≤ 523, which is also a positive integer, which is a positive integer, and \57x = 3, 4, 5, 4, 5, and all of these are all 3, 4, 4, 5, and all of 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 is a positive integer, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, & nbsp; (5 points) therefore, there are three schemes for the arrangement of vehicles: scheme 1: 3 vehicles of type A, 11 vehicles of type B and 6 vehicles of type C; scheme 2: 4 vehicles of type A, 8 vehicles of type B and 8 vehicles of type C; scheme 3: 5 vehicles of type A, 5 vehicles of type B and 10 vehicles of type C. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (7 points) (3) suppose that the sales profit is w 100 yuan, w = 8x · 12 + 6 (20-3x) · 16 + 5 [20-x - (20-3x)] · 10 = - 92x + 1920. ∵ w decreases with the increase of X, and x = 3, 4, 5 ∵ when x = 3, w max = 1644 (100 yuan) = 164400 yuan. A: to maximize the sales profit, we should use the first scheme in (2), that is, 3 vehicles for type A, 11 vehicles for type B, 6 vehicles for type C, and the maximum profit is 164400 yuan Yuan. (10 points)
A local product company organized 15 vehicles to ship a, B and C local products to other places for sale. According to the plan, all 15 vehicles will ship, and each vehicle can only ship the same product
The number of vehicles carrying a special local product is x, and the number of vehicles carrying B special local product is y. one vehicle of a special local product can hold 9 tons, and the profit per ton is 1500 yuan. Each vehicle of B special local product can hold 7 tons, and the profit per ton is 18000 yuan. Each vehicle of C special local product can hold 6 tons, and the profit per ton is 1000 yuan
(1) How many tons of local products have these 15 cars shipped?
(2) How many ten thousand yuan is the total profit after the sale of this batch of local products?
Car C: 15-x-y;
Loading capacity: 9x + 7Y + 6 * (15-x-y)
Profit: 0.15x + 0.18y + 0.1 * 6 * (15-x-y)
*: multiply sign;
A company decided to organize 21 vehicles to transport 120t of local a, B and C local products to Beijing. There are three types of vehicles available: A, B and C,
It is known that each type of car can be loaded with 2 local products, and each car is just full
Table: freight per vehicle of a, B and C
A 2 2 1500
B 4 2 1800
C 1 6 2000
① Let x cars of type A and Y cars of type B be used to find the functional relation of XY
② If there are no less than four cars of three models, what are the solutions?
③ In order to save the freight, which scheme in 2 should be adopted and the least freight should be calculated
This seems to be an applied problem in junior high school, which tests the basic equations and calculation ability. I haven't touched this problem for more than ten years, and the level has really dropped a lot. Let's set X cars of type A, y cars of type B, Z cars of type C; get the equation: 4x + 6y + 7z = 120
RELATED INFORMATIONS
- 1. A local product company organizes 20 vehicles to ship three kinds of local products of a, B and C for sale in other places. According to the plan, 20 vehicles will be shipped, and each vehicle can only ship the same kind of local products, and must be full. Suppose the number of vehicles carrying a kind of local products is x, and the number of vehicles carrying B kind of local products is y. according to the information provided in the table below, the number of vehicles carrying a kind of local products of a, B kind of local products of a, B type of local products of a, B type of local products of B is y Carrying capacity of each vehicle (ton) 8 65 Profit per ton of local products (100 yuan) 12 16 10 How many tons of local products have these 20 cars shipped? How many ten thousand yuan is the total profit after the sale of this batch of local products?
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