Question 1. Gama Energy meets the power demand of four cities by its three power plants. The capacities of plants and the demand of each city are given below. The below table shows the cost of transporting 1 million kWh of electricity from each plant to each city. Formulate a linear programming model to become a transportation plan that minimizes the total cost of meeting power demand. Question 2. Three raw materials are used to produce three products: a fuel additive, a solvent base, and a carpet cleaning fluid. The profit contributions are $40 per ton for the fuel additive, $30 per ton for the solvent base, and $50 per ton for the carpet cleaning fluid. Each ton of fuel additive is a blend of 0.4 tons of material 1 and 0.6 tons of material 3. Each ton of solvent base requires 0.5 tons of material 1, 0.2 tons of material 2, and 0.3 tons of material 3. Each ton of carpet cleaning fluid is a blend of 0.6 tons of material 1, 0.1 tons of material 2, and 0.3 tons of material 3. The production company has 20 tons of material 1, 5 tons of material 2, and 21 tons of material 3. Demand (kWh) City 1 45 City 2 20 City 3 30 City 4 30 Maximum supply (kWh) Plant 1 35 Plant 2 50 Plant 3 40 City 1 City 2 City 3 City 4 Plant 1 8 6 10 9 Plant 2 9 12 13 7 Plant 3 14 9 16 5 2 Suppose that the following data are available concerning the setup cost and the maximum production quantity for each of the three products: Product Setup cost Maximum production Fuel additive $200 50 tons Solvent base $50 25 tons Carpet cleaning fluid $400 40 tons This company is interested in determining the optimal production quantities to maximize its profit. Provide an integer linear programming model