Tamlin Architectural is building a new, green apartment building downtown. In order to maintain the building's eco-freindly status, the carbon footprint of the building's heating systems needs to be kept as low as possible. The architectural firm has two kinds of heating units available. A solar heater costs $13,000 provides 400 W of heat, and has a carbon footprint of 0.6. A heat pump costs $4,500, provides 800 W of heat, and has a carbon footprint of 4.2. The architects need at least 12,000 W of heat for the building, and cannot spend more than $261,000 on the heating system. How many of each type of heater should Tamlin Architectural use in order to meet the criteria while minimizing the carbon footprint? Can you formulate a linear programming model for this situation? Can you solve this model using graphical analysis? Can you display your graph and the solution parameters?