In the questions below, display formulas and the steps necessary to acquire a solution. 1. Find the minimum cost solution for the following transportation problem which has cost structure as:

To/From	P	Q	R	Availability
A	16	19	12	14
B	22	13	19	16
C	14	28	18	12
Requirement	10	15	17

2. Briefly describe the Simplex method, Goal Programming, and Integer Programming. 3. (a) The annual requirements for a particular raw material are 2,000 units costing Re. 1 each to the manufacturer. The ordering cost is Rs. 10 per order and the carrying cost 16% per annum of the average inventory value. Find and explain the economic order quantity and the total inventory cost per annum.

If this following example is incorrect, explain why. Total Inventory Cost = (2,000 units * Rs. 1) + ((2,000/500) * Rs. 10) + ((500/2) * Rs. 0.16)

Total Inventory Cost per annum = Rs. 2080 (b) The costs of placing an order are Rs. 150 per order. It is estimated that 1000 units will be used in the next 12 months. The carrying cost per month is Rs. 2.50. Assuming that the demand is deterministic and continuous and that no stock-outs are allowed, determine the optimal order quantity. If this following example is incorrect, explain why: EOQ = (2 * 1,000 * 150/2.50)

(300,000/2.50)

120,000

EOQ = 346.41

4. Based on the above, explain the following: If the following examples are incorrect, explain why: Time between the placing of orders = 1,000 units/347

Time between orders = 2.88 months

Re-order point = Average demand per month * procurement lead time

Average Demand per month = 1,000/12

Average Demand per month = 83.33

Re-order Point = 83.33 units * 1 month

Re-order Point = 83.33

What is the time between the placing of orders?

The procurement lead time is one month.

What is the re-order point based on the on-hand inventory level? 5. (a) Define "Critical path"with reference to PERT and CPM. (b) Define "Slack time"with reference to PERT and CPM. (c) Define "Resource Levelling" with reference to PERT and CPM. (d) Define "Dummy activity" with reference to PERT and CPM. 6. An architect has been awarded a contract to prepare plans for an urban renewal project. The job consists of the following activities and their estimated value. Demonstrate how the critical path arrow diagram for this project should look, indicate the critical path, and calculate the total slack and free slack for each activity.

Job	Description	Predecessor	Expected time in days
A	Prepare preliminary sketches	NA	2
B	Outline specifications	NA	1
C	Prepare drawings	A	3
D	Write specifications	A B	2
E	Run prints	C D	1
F	Have specifications printed	B D	3
G	Assemble bid package	E F	1