In November 2022, regional car rental agency Penny Rent A Car (PRAC) rented out 2050 cars per day at a rate of $60 per day. This summer, for each $2 increase in rate, 30 fewer cars are rented. (i) At what rate should the cars be rented to produce the maximum income? (ii) How many cars are supposed to be rented out? (iii) What is the maximum income? (iv) If the management considers Plan A: increasing $2 more than the optimized rate in part (i), or Plan B: decreasing $2 less than the optimized rate in part (i), which plan, A or B, will generate more income? Explain your reason