bAn economy consists of two industries X and Y with each industry producing a

# Ban economy consists of two industries x and y with

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(b)An economy consists of two industries X and Y with each industry producing a single product. The table shows the use and production of X and Y over some fixed period of time. TO X Y Consumer Demand FROM X 70 35 95 Y 40 60 60 (i) The final demand for A increases by 40 units and B decreases by 25%. Determine the new total output by the two industries so as to satisfy the new final demand. (10 Marks) Page 2 of 5
Question Three (a)Given the information below of a project managed by X-cut company. Activity Preceeding Activity Duration (Days) A - 3 B - 3 C - 7 D A 1 E D, J 2 F B 2 G C 1 H E,F,G 1 J B 1 You are required: (17 Marks) (i) To draw a network diagram for the project (ii) Determine the critical path (iii) Calculate ES, EF, LS and LF times for each activity. (b)Briefly discuss the relation between the arrival and the service rate in a queue. (3 Marks) Question Four (a)Solve the linear programming problem. (12 Marks) Page 3 of 5
Minimize: Z = 2x + 3y Subject to: 3x + y ≥ 15 0.5x + y ≥ 10 x+ y ≥ 13 y ≥4 (b)Solve the following equation using the matrix algebra method. (5 Marks) 2x + y =1 x + 2y = -1 (c) In quantitative models, what is the difference between feasible solution and optimal solution? (2 Marks) (d)In a network, what is a dummy activity? (1 Mark) Question Five (a)Perform the following (i) Find dy/dx if Y = 1 + (x 3 + 2x) 4 (4 Marks) x 2 Page 4 of 5
(ii) 1 2 ( x x 2 ) dx (5 Marks) (b)A service station is open for 24 hours. During this time customers arrive at the filling station with a mean of 30 per hour. The service time has a mean of 3 customers in 5 minutes. Calculate the (i) Mean service (rate) per hour. (4 Marks) (ii) Traffic Intensity (c) Define the term game theory and illustrate THREE types of games. (5 Marks) (d)What is the importance of input-output analysis is an economy? (2 Marks) Page 5 of 5

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