The first is the differential equation model. The necessary assumption of the model is that n is large enough to think that the propagation process is continuous.

Suppose the number of people who believe in rumors is y, then

dy/dt=k(n-y)

Y= 1 when t=0.

First order linear ordinary differential equation, I don't understand.

The second is optimization problem, that is, integer optimization of single objective function.

Let the output of four quarters be X 1, X2, X3 and X4 respectively.

Minimum 5000 * (x1+x2+x3+x4)+(x1-3000) *1500+(x2-3000) *1500+(x3-3000).

Science and technology.

x 1 & gt； 3000

x2 & gt3000

x3 & gt3000

x4 & gt3000

x 1 & lt； 4500

x2 & lt4500

x3 & lt4500

x4 & lt4500

x 1+x2 & gt； 7500

x 1+x2+x3 & gt； 1 1000

x 1+x2+x3+x4 & gt； 16000

The objective function is the sum of normal production cost, overtime cost and inventory cost. I don't know whether the first four items in the constraint need to be added, depending on the specific meaning of the problem, but it should not affect the result, so I can paste the above items directly into lindo to solve it.

As for the restatement of the problem, you can just make it up yourself. The model can be fooled, and there is no big problem. ...