Howie’s Carpet World. Howie’s Carpet World has just received an order for carpets for a new office building. The order is for 4,000 yards of carpet 4-feet wide, 20,000 yards of carpet 9-feet wide, and 9,000 yards of carpet 12-feet wide. Howie can buy 2 kinds of carpet rolls from his supplier, namely 14 feet wide carpet and 18 feet wide; and Howie will cut the carpet for the new office building order from whatever carpet he buys from his supplier. The 14 feet wide carpeting comes in rolls of 100-yards long and costs $1000 per roll; the 18 feet wide carpeting also comes in rolls of 100-yards long, but it costs $1400 per roll. Howie needs to determine how many of the two types of carpet rolls to buy from his supplier and how they should be cut in order to minimize his cost of filling the order.

Formulate this problem as an algebraic linear integer optimization model. Be sure to define your variables.