Hourly demand: 70 items Maximum production rate: (850/3) items/hr. Production cost: $1 per item Hourly holding cost: $0.10 per item Set-up cost: $270. A company producesan item. Assume that shortages are not allowed, and the round-robin ELSP conditions apply. After ?nishing a production run of items, it takes 10 minutes to set-up the machine for the next item. Assume the machine is either setting up, processing at maximum rate, or idle.

(a) On a single diagram, plot and label the optimal inventory trajectories as a function of time.

(b) How many items should be produced during each production run?

(c) Determine the maximum on-hand inventory.

(d) Determine the optimal number of production runs, on average, each hour.

(e) Determine the optimal total hourly cost.

(f) Determine the average fraction of time the machine will spend idle.