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One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.
The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is
[2011]
- a)0
- b)1360
- c)1500
- d)2000
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
One unit of product P1 requires 3 kg of resource R1 and 1 kg resource ...
Because second constraint is redundant in nature. Therefore, resource R2 has no effect on the feasible solution.
Most Upvoted Answer
One unit of product P1 requires 3 kg of resource R1 and 1 kg resource ...
Given:
- 1 unit of product P1 requires 3 kg of resource R1 and 1 kg of resource R2.
- 1 unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2.
- The profits per unit by selling product P1 and P2 are Rs. 12000 and Rs. 3000 respectively.
- The manufacturer has 90 kg of resource R1 and 100 kg of resource R2.
To find:
The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg.
Solution:
To find the dual price of resource R2, we need to use the concept of linear programming and solve the given problem using the Simplex method.
Step 1: Formulate the linear programming problem.
Let x be the number of units of product P1 produced.
Let y be the number of units of product P2 produced.
The objective function to be maximized is:
Z = 12000x + 3000y
Subject to the following constraints:
3x + 2y ≤ 90 (resource R1 constraint)
x + 2y ≤ 100 (resource R2 constraint)
x ≥ 0, y ≥ 0 (non-negativity constraints)
Step 2: Solve the linear programming problem using the Simplex method.
Using the Simplex method, we can solve the above problem to find the optimal values of x and y.
Step 3: Interpret the results.
After solving the linear programming problem, we will obtain the optimal values of x and y, which represent the number of units of product P1 and P2 produced. From these values, we can calculate the dual price of resource R2.
In this case, the dual price of resource R2 is 0 (option A).
Conclusion:
The dual price of resource R2, i.e. the unit worth of resource R2 in Rs per kg, is 0. This means that the resource R2 does not have any economic value or scarcity in the given problem.
- 1 unit of product P1 requires 3 kg of resource R1 and 1 kg of resource R2.
- 1 unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2.
- The profits per unit by selling product P1 and P2 are Rs. 12000 and Rs. 3000 respectively.
- The manufacturer has 90 kg of resource R1 and 100 kg of resource R2.
To find:
The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg.
Solution:
To find the dual price of resource R2, we need to use the concept of linear programming and solve the given problem using the Simplex method.
Step 1: Formulate the linear programming problem.
Let x be the number of units of product P1 produced.
Let y be the number of units of product P2 produced.
The objective function to be maximized is:
Z = 12000x + 3000y
Subject to the following constraints:
3x + 2y ≤ 90 (resource R1 constraint)
x + 2y ≤ 100 (resource R2 constraint)
x ≥ 0, y ≥ 0 (non-negativity constraints)
Step 2: Solve the linear programming problem using the Simplex method.
Using the Simplex method, we can solve the above problem to find the optimal values of x and y.
Step 3: Interpret the results.
After solving the linear programming problem, we will obtain the optimal values of x and y, which represent the number of units of product P1 and P2 produced. From these values, we can calculate the dual price of resource R2.
In this case, the dual price of resource R2 is 0 (option A).
Conclusion:
The dual price of resource R2, i.e. the unit worth of resource R2 in Rs per kg, is 0. This means that the resource R2 does not have any economic value or scarcity in the given problem.
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One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer?
Question Description
One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer?.
One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer?.
Solutions for One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is[2011]a)0b)1360c)1500d)2000Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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