A utility company supplies drinking water to a community, which demands at least 10,000 m3 of water daily, from two pumping stations (A and C). Station A has a maximum supply capacity of 18,000 m3 , while station C has a maximum capacity of 20,000 m3 per day. Due to operational constraints, station C must supply at least 6,000 m3 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 communitys water demand at the lowest possible cost, while complying with the systems requirements.

What would be the dual or shadow price of the constraint representing the maximum supply capacity of station A, and why?

What would be the allowable increase for the dual price of such a constraint mentioned in question 7, and why?