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in Linear Programming by (3.3k points)
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The graph of a linear programming problem is given below. The shaded region is the feasible region. The objective function is Maximise; Z = px + qy

(i) What are the co-ordinates of the corners of the feasible region?

(ii) Write the constraints. 

(iii) If the Max. Z occurs at A and B, what ¡s the relation between p and q? 

(iv) If q = 1, write the objective function. 

(v) Find Max. Z

1 Answer

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Best answer

(i) From the figure the feasible region is OABC. Then the comer points are; A is (5, 0), B is (3, 4), C is (0, 5) and O (0, 0) 

(ii) The constraints are 2x + y < 10, x + 3y < 15, x < 0, y < 0 

(iii) Given; Z = px + qy

Corner points

Value of Z

O

Z=p(0)+q(0) = 0

A

Z = p(5) + q(Q) = 5p

B

Z = p( 3)+g(4) = 3p + 4q

C

Z = p(0) + q(5) = 5q

Since maximum at A and B we have; 

⇒ 3p + 4q = 5p ⇒ 2p = 4q ⇒ p = 2q 

(iv) When q = 1, then p ⇒ 2q ⇒ p = 2 

Objective function is; Z = 2x + y 

(v) We have; Z px + qy at B Z has maximum 

⇒ Z = 2(3) + 4 

= 10

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