A manufacturer manufactures two types of tea-cups, A and B. Three machines are needed for manufacturing the  tea cups. The time in minutes required for manufacturing each cup on the machines is given below:
Each machine is available for a maximum of six hours per day. If the profit on each cup of type A is Rs. 1.50 and that  on each cup of type B is Rs. 1.00.  Then answer the following questions:

This question is inspired from Misc 4 - Chapter 12 Class 12 (Linear Programming)

Slide25.JPG

Slide26.JPG
Slide27.JPG Slide28.JPG

 

Question 1

Let x be the number of A type tea cups and y be the number of B type tea cups.  Then the objective function associative with the given problem is:

(a) Max. Z = 1.50 x + y  

(b) Max. Z = x + 1.50 y

(c) Min. Z = 1.50 x – y  

(d) Min. Z = x – 1.50 y.

Slide29.JPG

 

Question 2

Let x be the number of A type tea cups and y be the number of B type tea cups.  Then the constraints associative with the given problem are:

(A) 2x + y ≥ 60
        x ≤ 20
      2x + 3y ≤ 120

(B) 2x + y ≤ 60
        x ≤ 20
      2x + 3y ≤ 120

(A) 2x + y ≤ 60
        x ≥ 20
      2x + 3y ≤ 120

(A) 2x + y ≤ 60
        x = 20
      2x + 3y ≥ 120

Slide30.JPG

 

Question 3

The non-negative conditions are given as:

(a) x ≥ 0, y ≥ 0  

(b) x ≥ 0, y ≤ 0

(c) x ≤ 0, y ≥ 0  

(d) x ≤ 0, y ≤ 0

Slide31.JPG

 

Question 4

Feasible region has how many corner points?

(a) 3   

(b) 4

(c) 5  

(d) 6

Slide32.JPG Slide33.JPG

 

Question 5

The Maximum Profit is :

(a) Rs. 40  

(b) Rs. 50

(c) Rs. 30  

(d) Rs 52.5
Slide34.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question A manufacturer manufactures two types of tea-cups, A and B. Three machines are needed for manufacturing the tea cups. The time in minutes required for manufacturing each cup on the machines is given below: Each machine is available for a maximum of six hours per day. If the profit on each cup of type A is Rs. 1.50 and that on each cup of type B is Rs. 1.00. Then answer the following questions: Let Number of cups of Type A = x Number of cups of Type B = y Machine I Time required on Type A → 12 Min Type B → 6 Min Max Available Time = 360 min ∴ 12x + 6y ≤ 360 2x + y ≤ 60 Machine II Time required on Type A → 18 Min Type B → 0 Min Max Available Time = 360 min ∴ 18x + 0.y ≤ 360 x ≤ 20 Machine III Time required on Type A → 6 Min Type B → 9 Min Max Available Time = 360 min ∴ 6x + 9y ≤ 360 2x + 3y ≤ 120 As we need to maximize the Profit Given that the profit on each cup of type A is Rs. 1.50 and that on each cup of type B is Rs. 1.00 ∴ Z = 1.50 x + 1.00 y Combining all constraints : Max Z = 1.5x + y Subject to constraints, 2x + y ≤ 60, 2x + 3y ≤ 120, x ≤ 20, & x ≥ 0 , y ≥ 0 Question 1 Let x be the number of A type tea cups and y be the number of B type tea cups. Then the objective function associative with the given problem is: (a) Max. Z = 1.50 x + y (b) Max. Z = x + 1.50 y (c) Min. Z = 1.50 x – y (d) Min. Z = x – 1.50 y. Here, we need to Maximize Z = 1.5x + y So, the correct answer is (a) Question 2 Let x be the number of A type tea cups and y be the number of B type tea cups. Then the constraints associative with the given problem are: (A) ■8(2𝑥+𝑦≥60@𝑥≤20@2𝑥+3𝑦≤120) (B) ■8(2𝑥+𝑦≤60@𝑥≤20@2𝑥+3𝑦≤120) (C) ■8(2𝑥+𝑦≤60@𝑥≥20@2𝑥+3𝑦≤120) (D) ■8(2𝑥+𝑦≤60@𝑥=20@2𝑥+3𝑦≥120) Constraints in our LPP are 2x + y ≤ 60, 2x + 3y ≤ 120, x ≤ 20, So, the correct answer is (b) Question 3 The non-negative conditions are given as: (a) x ⤶7≥ 0, y ⤶7≥ 0 (b) x ⤶7≥ 0, y ≤ 0 (c) x ≤ 0, y ⤶7≥ 0 (d) x ≤ 0, y ≤ 0 Non-negative conditions are where x, y cannot be negative Therefore, they are x ⤶7≥ 0, y ⤶7≥ 0 So, the correct answer is (a) Question 4 Feasible region has how many corner points? (a) 3 (b) 4 (c) 5 (d) 6 Our LPP is Max Z = 1.5x + y Subject to constraints, 2x + y ≤ 60, 2x + 3y ≤ 120, x ≤ 20, & x ≥ 0 , y ≥ 0 Since feasible region as 5 corner points – A, B, C, D, O So, the correct answer is (c) Question 5 The Maximum Profit is : (a) Rs. 40 (b) Rs. 50 (c) Rs. 30 (d) Rs 52.5 Finding values at corner points Hence, Maximum Profit = Rs. 52.50 So, the correct answer is (d)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.