A two variables linear programming problem (100 points) A utility company supplies drinking water to a community, which demands at least 10,000m3 of water daily, from two pumping stations (A and C). Station A has a maximum supply capacity of 18,000m3, while station C has a maximum capacity of 20,000m3 per day. Due to operational constraints, station C must supply at least 6,000m3 of water. In addition, since both stations handle different purity levels, the water authority stated that the amount of water supplied by station A must be at least one-third of the amount supplied by station C. The operational costs of supplying one cubic meter (m3) of water from the stations are 2000($/m3) from A and 1000($/m3) from C. Please formulate a linear programming model that allows finding the optimal way to meet the community's water demand at the lowest possible cost, while complying with the system's requirements. The following questions need to be answered (elaborate on your answers): 3. (5 points) Classify the constraints into active and non-active. 4. (10 points) The company is considering expanding the supply capacity of one of the two stations and wants you to make a recommendation in this regard; Write: which station to expand and by what amount? 5. (10 points) How much would the total costs increase if the capacity of station A were reduced by half, that is, 9000m3, and explain why