1 The demand for a certain item is 12 units per period. No shortages are to be allowed. Holding cost is $0.02 per unit per period. Demand can be met either by purchasing or manufacturing, with each source described by the data given in the table. PURCHASE MANUFACTURE Procurement Lead Time 18 periods 13 periods Item Cost $11.00 $9.60 Procurement Cost $20.00 $90.00 Replenishment Time Any amount 25units/period Find the minimum-cost procurement source and calculate its economic advantage over its alternative source.

2. An item with a demand of 300 units per period is to be purchased and no shortages are allowed. The item costs $1.30, holding cost is $0.02 per unit per period, and it costs $28.00 to process a purchase order. Each item consumes 2 cubic feet of warehouse space. The warehouse contains 1,500 cubic feet of space. Find the minimum-cost procurement quantity and procurement level under this restriction if the lead time is 2 periods. What is the cost penalty due to the warehouse restriction?

3. The arrival rate for a certain waiting-line system obeys a Poisson distribution with a mean of 0.5 unit per period. It is required that the probability of one or more units in the system not exceed 0.20. If the cost of waiting is $5.00 per unit per period, and the service facility costs $2.50 per unit served, what is the total system cost? If the service rate is doubled at a total cost of $3.50 per unit served, what is the total system cost?

4. Trucks arrive at a loading dock in a Poisson manner at the rate of 3.5 per day. The cost of waiting per truck per day is $168. A three-person crew that can load at a constant rate of four trucks per day costs $224 per day. Compute the total system cost for the operation.

5. A group of 12 machines are repaired by a single repairperson when they break down. Each machine yields a profit of $5.20 per hour while running. The mechanic costs the firm $20.40 per hour, including overhead. At the present time no preventive maintenance is used. It is proposed that one technician be employed to perform certain routine maintenance and adjustment tasks. This will cost $16.60 per hour but will reduce the service factor from 0.13 to 0.08. What is the economic advantage of implementing preventive maintenance?

6 . Specify the dimensions of the sides of a rectangle of perimeter p so that the area it encloses will be maximum.

question 7. Why is it essential that be greater than in a probabilistic waiting line process