please solve manually or in ampl

Demand for electricity over the next month is projected to be constant and exactly 424MW. There are 7 power plants that, when turned on for the month, can be continuously regulated to produce between li and uiMW for i=1,,7. There is a fixed cost of si dollars for every power plant i that is turned on, and a variable cost of ci dollars per MW. 1. Write a mixed-integer linear optimization model to find a minimum-cost plan to operate the power plants that guarantees that the demand is satisfied. (You do not need to solve the model.) 2. Add a linear constraint: At least 3 plants need to be turned on. 3. Add a linear constraint: Plant 3 and 7 cannot be both turned on. 4. Add a linear constraint: If plants 4 and 5 are both on, then also plant 6 must be on