QUESTION 1
A manufacturer must design a new material that must contain 2 components referred to as component A and component B. Each gram of component A contains 2 units of carbon and 2 units of steel and each gram of component B contains 1 unit of carbon and 4 units of steel. The cost of component A is Rs 4 per gram and the price of component B is Rs 5 per gram. Customers' specification requires that the material should contain at least 7 units of carbon and at least 10 units of steel.
(a) Formulate the complete linear programming model for the manufacturer's problem showing clearly the objective function and constraint sets given that the cost of the new material should be kept at the minimum possible level.
(b) Use the graphical method to calculate the combination of components A and B that actually minimizes cost.
QUESTION 2
Betty Edwards is a college student whose summer job involves selling magazine subscriptions. She currently has 4 magazine subscriptions available and, according to company policy, she can sell only one subscription to any customer. She currently has 4 prospective customers, and these four customers are willing to pay different prices for the subscriptions to the four magazines. The profit table associated with sales of the four magazine subscriptions to the 4 customers is as follows.
|
Magazine
|
Customer
|
|
I
|
2
|
3
|
4
|
|
1
|
4
|
6
|
9
|
7
|
|
2
|
7
|
2
|
3
|
6
|
|
3
|
5
|
5
|
6
|
10
|
|
4
|
8
|
4
|
2
|
4
|
(a) What is the objective of the assignment model and its main characteristics?
(b) Suggest an optimal assignment and the total maximum profit for Betty Edwards. Explain clearly all the steps involved in obtaining the optimal assignment
QUESTION 3
(a) Describe the various costs associated with inventory control
(b) Define Economic Order Quantity (EOQ) and outline the assumptions of the basic EOQ Model
(c) At the Mahebourg Museum, the demand for guide books is 1200 per year. The books are purchased from a supplier for Rs 9 each. Order costs are Rs 10 per order. The annual cost of carrying stock is Rs 2.50 per unit. Assume that there are 250 working days in the year. Determine the following-
(i) EOQ
(ii) The number of orders that should be placed each year
(iii) The time between orders
(iv) The minimum total annual cost