1) Filing cabinet A has a footprint (floor space requirement) of 4 square ft. Cabinet B has a footprint of 6 square feet. The office only has 30 square feet that can be used for cabinets. Write a constraint on the number of cabinets that should be installed.

2) An aid agency is buying generators for storm survivors. The resettlement area requires at least 15,000 kWh. Generator A is rated at 150 kWh, generator B is rated at 175 kWh. Write a constraint prescribing the number of generators of each type that can be purchased.

3) Larry's Yard Care mows lawns, trims hedges and winterizes flower beds. The company charges $15 per hour for mowing, $12 per hour for trimming, and $25 per hour for winterizing. Write an hourly income function for the company, in terms of the number of jobs, by type, that were underway during that hour.

4) Thunder Garage assembles diesel engines for cars and trucks. The car engines have four cylinders, the truck engines have six. Each cylinder in a diesel engine requires a separate fuel injector. The supplier can only provide 1300 injectors per month. Write a constraint prescribing the number of each type engine that can be produced.