A car repair shop chain plans to expand by opening several new repair shops. The chain operates two types of car repair shops: Quick Lube and Full Service. A Quick Lube shop costs $$100,000$ to build, requires $5$ employees and has an expected annual revenue of $$200,000.$ A Full Service shop costs $$150,000$ to build, requires $15$ employees and has an expected annual revenue of $$500,000.$ The chain has $$2,400,000$ available for construction in the expansion budget. Labour contracts require that they hire no more than $210$ employees, and licencing restrictions require that they open no more than $20$ new car repair shops. How many repair shops of each type should the chain open in order to maximize the expected revenue? What is the maximum expected revenue? How much of their construction budget will they use and how many employees will they hire?