Question 1 (20 marks) Considering the following company Delux, which is a large food store based in California. a) Delux is planning to use a lockbox system to speed up collections from its customers. The system is expected to reduce the average collection time by 2.8 days. On an average day, your firm receives 2,419 checks with an average value of $1,287 each. The daily interest rate on Treasury bills is 0.016 percent. The bank charge per check is $0.30. What is the net present value of this lockbox arrangement? Should Delux accept this system? What is the amount of the annual net savings if this plan is adopted? (13 marks) b) Your neighbor goes to the post office once a month and picks up two checks, one for $18,000 and one for $4,000. The larger check takes 4 days to clear after it is deposited; the smaller one takes 6 days. Assume 30 days per month. What is the weighted average delay? (7 marks)