A machine shop purchases spare parts for several machines at the rate of 1000 per year. The cost of each part is $20, and the cost of placing an order is $20. the inventory carrying cost is$2.5 per unit per year. The shortage cost is $5.5 per unit per year. Assume that the demand (x) during lead time follows an exponential distribution with a p.d.f of e^0.05x over the range 0 to 200. The shortage cost per unit short is $2 based on the average shortage. Find Q* and r*. Assume that shortages are backordered.