Q4 of 17 Page 12

Solve the following L.P.P. graphically :

Minimize


Subject to


Constraints



and [CBSE 2017]

Minimize

Z = 5x + 10y


Subject to constraints


x + 2y ≤ 120


x + y ≥ 60


x – 2y ≥ 0


and x , y ≥ 0


Firstly, we draw the graph of the line x + 2y = 120














x



0



120



y



60



0



Put (0,0) in the inequality x + 2y ≤ 120, we get


0 + 2 × 0 ≤ 120


⇒ 0 ≤ 120 (which is true)


So, half plane is towards the origin.


Secondly, graph of the line x + y = 60














x



0



60



y



60



0



Put (0,0) in the inequality x + y ≥ 60, we get


0 + 0 ≥ 60


⇒ 0 ≥ 60 (which is false)


So, half plane is away from the origin.


Thirdly, draw the graph of line x – 2y = 0














x



0



10



y



0



5




On solving equations x – 2y = 0 and x + y = 60, we get B(40, 20)


and on solving equations x – 2y = 0 and x + 2y = 120, we get C(60, 30).


Feasible Region is ABCDA.



So, the minimum value of Z is 300 at the point (60, 0)


More from this chapter

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2

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and a half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ₹ 100 and that on a bracelet is ₹ 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced. [CBSE 2017]

 3

Maximise z = x + 2y

Subject to the constraints


x + 2y ≥ 100


2x – y ≤ 0


2x + y ≤ 200


x, y ≥ 0


Solve the above LPP graphically. [CBSE 2017]

 5

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.[CBSE 2011]

 6

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.

(i) What number of rackets and bats must be made if the factory is to work at full capacity?


(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity. [CBSE 2011]