Mathematics (M) (950) Third Term Masyati Binti Karim

Quiz 1: Mathematics (M) (950)

Answer all questions. All necessary working should be shown clearly.

1. A small cellular phone company manufactures two popular models, for which the demand for both models is much greater than the current supply. The company manager has production constraints and profit opportunity listed in the following table.

Model 1 Model 2 Maximum hours available per month

Assembly time per unit 1 hour 1 hour 40 000

Test time per unit hour hour 10 000

Profit per unit RM 60 RM 90 -

(a) Determine the linear programming model to obtain the greatest monthly profit that the company can make without increasing its current facilities. [3 marks]

(b) Use the simplex method to obtain the solution for the linear programming problem. [9 marks]

2. An assembly process to manufacturing certain gadget consists of seven tasks as follows:

Task Predecessors Duration (in hours)A - 2B - 1C A 1D A, B 1E A, B 6F C 3G D, E 2

(a) Draw an AOA network diagram for the assembly process. [3 marks](b) Determine the critical path of the assembly process and the minimum assembly duration. [8 marks]

3. Consider the following two-person, zero-sum game. Payoffs are winnings for Player A. Identify the pure strategy solution. Hence, state the value of the game?

Player B

Player A8 5 72 4 10

[3 marks]

Mathematics (M) (950) Third Term Masyati Binti Karim

4. Eastside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Eastside's generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year (12 000 units annually). Assume that the ordering costs are RM 25 per order, the unit cost is RM 2.50 per component, and annual holding costs are 20% of the value of the inventory. Eastside has 250 working days per year and a lead time of 5 days.

(a) Find the EOQ for this component. [3 marks](b) Determine the reorder point and the cycle time. [3 marks](c) Find the total annual holding and ordering costs associated with your recommended EOQ. [5 marks]

5. Suppose that Eastside Auto of Question 4, with D = 12 000 units per year, RM 0.50, and RM 25.00, decided to operate with backorder inventory policy. Backorder costs are estimated to be RM 5.00 per unit per year.(a) Find the minimum cost order quantity. [3 marks](b) Determine the maximum number of backorders. [2 marks](c) Find the maximum inventory and the cycle time. [6 marks](d) Hence, calculate the total annual cost. [4 marks]