A workman$$s wages for a guaranteed $44$ hours week is $`75$ per hour. The estimated time to produce one article is $30$ minutes and under an incentive plan, the time allowed is increased by $20$ per cent. During a week, a worker produced $100$ articles.

Calculate the wages under: $($a$)$ Time rate, $($b$)$ Rowan system and $($c$)$ Halsey system.