Learning Curve Effect (20 points): While a worker gains experience with time spent on a production line the throughput of the line increases exponentially or the unit production time decreases, but the learning rate varies depending on the situation. The cost of first two additive manufacturing (AM) units is $12,000. Because of the new innovative project, the learning rate was estimated as 80% where = is the cost of producing the nth unit and K is the cost producing the first unit. The company wants to produce just 500 AM units in the first batch. [Assume at any production level N, the production doubles].

(a) What is the cost of the first item?

(b)How much will it cost to produce 500th unit?

(c) How much will it cost on the average to 500 units?

(d) How much will the company save per unit on the average cost of production if its batch size is 1000 units?