Question 3 - Case Based Questions (MCQ) - Chapter 12 Class 12 Linear Programming

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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)