You are the head of a building department . Your department is making final inspections of two types of new commercial buildings --gas stations and restaurants . Final inspections involve the work of three separate inspectors : a plumbing inspector , an electrical inspector , and a building inspector . The plumbing inspector requires 4 hours to inspect a gas station and 2 hours to inspect a restaurant . The electrical inspector requires 2 hours to inspect a gas station and 6 hours to inspect a restaurant . The building inspector requires 4 hours to inspect a gas station and 6 hours to inspect a restaurant . Considering the time required for other duties , the plumbing inspector has 28 hours a week available for inspections ; the electrical inspector has 30 hours available and the building inspector has 36 hours available . You want to inspect as many commercial buildings as possible each week . Set up this problem as a linear programming problem .