[14] UPS2012 2013 - Lecture notes 1 PDF

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MID-SEMESTER EXAMINATION PAPER UPS 2012/2013 1.

Determine the system of inequalities that define the feasible region R in the diagram below. y y=x

12

R 2 x 9

0

[5 markah]

2

2.

Given the demand function

D( x )=−x −14 x +17 and the supply function

S ( x )=x 2 +1 . Find (a)

the market equilibrium point. [4 markah]

(b)

the producer’s surplus. [3 markah]

3.

In the production of two types of toys, a factory uses two machines, A and B. The time required to produce the first type of toy is 6 hours and 8 hours in machines A and B respectively. The time required to make the second type of toy is 8 hours and 4 hours in machines A and B respectively. The available time for the machines A and B are 480 hours and 320 hours respectively. The operational cost for each toy of the first and second type produced are RM12 and RM4 respectively where the minimum capital allocated to produce the toys is RM240. Profit gained in the first type of toy is RM5 while that on the second type of toy is RM3.

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MID-SEMESTER EXAMINATION PAPER UPS 2012/2013

(a) Summarise the above information in a suitable table. [3 marks] (b) If x and y represents the number of the first type and the second type of toys which were produced respectively, determine the objective function to maximize the profit and formulate the given information in the form of linear programming model. [4 marks]

4.

Find the minimum value of the function

to

the constraint

2 2 f ( x , y ) =4 x +3 y −4 x −10 y +4 xy

subject

x + y =30 by using the method of Langrange multiplier. [12 marks]

END OF QUESTION PAPER

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MID-SEMESTER EXAMINATION PAPER UPS 2012/2013

ANSWERS :

1.

2.

(i)

x≥0 and y≥0

(ii)

(iv)

y >2

(v)

(a)

(1,2)

(b)

y≤x 4 x+3 y>36

(iii)

x...