1. The problem statement, all variables and given/known data A factory has stocked a lot of pipes (sufficient). Each standard pipe is 5-meter long. But this kind of pipe cannot be used directly. We should cut them into three types: 140cm, 95cm and 65cm. In addition, the proportion of these three types of pipes must be 2:4:1. In other words, each product needs two 140cm-long pipes, four 95cm-long pipes and one 65cm-long pipe. It is assumed that the pipes we cut down must be proportional. Now, this factory wants to manufacture K products with least pipes. Formulate this problem as an linear programming model. 2. Relevant equations 3. The attempt at a solution I have got a problem on letting the decision variable. I have tried to let there are i 140cm part, j 95cm part and g 65cm part, so that the remaining part of a standard pipe would be 500-x_ijg. But I don't know x_ijg is relevant to the total number of pipes or not. Hope someone helps. Thanks.