The manager of City Carpet has just received an order for carpets for a new office block. The order is for 1500 m of carpet 2 m wide, 6000 m of carpet 3 m wide, and 3000 m of carpet 4 m wide. The manager can manage two kinds of carpet rolls, which he needs to cut to fill this order. One type of roll is 6 m wide and 30 m long, and the second is 8 m wide and 30 m long. It costs $1500 per roll for the first type and $2000 per roll for the second type. City Carpet needs to determine how many of the two types of carpet rolls to buy and how they should be cut. Formulate the problem as an integer programming model in order to minimize the cost of carpets.