In an electronics company, there is a new production line constructed to work with five shifts in which $3$ units of television can be produced per $20$ minutes. Upper management decides to work five shifts a day, each containing $4$ hours, considering the demand from the market. However, some problems were encountered such as $50$ defective parts being produced, and the line had to be stopped for one hour each in shift due to machine breakdowns.

a$)$ What is the design capacity per day for the line producing televisions?

b$)$ What is the effective capacity per day for the line producing televisions?

c$)$ What is the actual output on the day for the line producing televisions?

d$)$ What is the company's capacity utilization relative to both design and effective capacity, when actual output produced in a day?