Current location - Training Enrollment Network - Mathematics courses - Math problem: There are 50 containers with uniform specifications in a warehouse to be sent to the dock by the transportation company.
Math problem: There are 50 containers with uniform specifications in a warehouse to be sent to the dock by the transportation company.
Suppose there are three kinds of trucks, A, B and C, which can transport 1, 2 and 3 containers at a time, and let A, B and C transport X, Y and Z trucks respectively, then there are:

① formula: x+y+z = 20 ② formula: x+2y+3z = 50.

②-① Formula ③:y+2z = 30 can be obtained.

3× ①-② can get ④ formula: 2x+y = 10.

④-③ The formula ⑤:2z-2x = 20→z = x+ 10 can be obtained.

The following formula can be obtained: ③ Formula: y+2z = 30 (available: Z≤ 15).

④ Formula: 2x+y = 10

⑤ formula: x+10 = z.

So there is the following answer:

1. Suppose X = 1, then Y = 8, Z = 1 1, and the cost =1×120+8×160+65438.

2. If X = 2, then Y = 6, Z = 12, and cost = 2×120+6×160+12×180 = 3360;

3. Suppose X = 3, then Y = 4, Z = 13, and the cost = 3x120+4x160+13x180 = 3340;

4. Suppose X = 4, then Y = 2, Z = 14, and the cost = 4×120+2×160+14×180 = 3320;

5. Suppose X = 5, then Y = 0, Z = 15, and the cost = 5×120+0×160+15×180 = 3300;

Therefore, the freight car scheduling that can hold 1, 2, and 3 pieces at a time: 5, 0, and 15 respectively.

* * * There are five arrangements.

The fifth kind of freight is the least, and the lowest freight is 3300.

(In fact, according to formulas ③, ④ and ⑤, it can be concluded that every time X increases 1 vehicle, Y decreases by 2 vehicles and Z increases 1 vehicle).

The unit marginal cost MC =/kloc-0 /×120-2×160+/kloc-0 /×180 =-20.

Therefore, when y is the smallest, the cost is the lowest.