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A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be
[2004]
- a)1000, 500
- b)800, 600
- c)500, 1000
- d)1000, 1000
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A company produces two types of toys : P and Q. Production time of Q i...
Zmax = 3P +5Q
subject to
P+ 2Q ≤ 2000
P+Q ≤ 1500
Q ≤ 600
P,Q ≥ 0
Feasible solution (O A B C D) Since At point A (1500,0) Z = 3 × 1500 + 5 × 0 = 4500
At Point B (1000, 500) Z = 3 × 1000 + 5 × 500 = 5500
At point C (800, 600) Z = 3 × 800 + 5 × 600 = 5400
At Point O (0, 600) Z = 3 × 0 + 5 × 600 = 3000
Hence Z in maximum at B (1000,500) P = 1000 units Q = 500 units
subject to
P+ 2Q ≤ 2000
P+Q ≤ 1500
Q ≤ 600
P,Q ≥ 0
Feasible solution (O A B C D) Since At point A (1500,0) Z = 3 × 1500 + 5 × 0 = 4500
At Point B (1000, 500) Z = 3 × 1000 + 5 × 500 = 5500
At point C (800, 600) Z = 3 × 800 + 5 × 600 = 5400
At Point O (0, 600) Z = 3 × 0 + 5 × 600 = 3000
Hence Z in maximum at B (1000,500) P = 1000 units Q = 500 units
Most Upvoted Answer
A company produces two types of toys : P and Q. Production time of Q i...
The Problem
A company produces two types of toys, P and Q. The production time of Q is twice that of P. The company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys of any type per day. Toy type Q requires an electric switch, which is available at a rate of 600 pieces per day. The company makes a profit of Rs. 3 and Rs. 5 on type P and Q toys, respectively. The task is to determine the daily production quantities of P and Q toys that will maximize the company's profits.
Assumptions
Before proceeding with the solution, let's make some assumptions:
1. The production time required for P and Q toys is measured in time units.
2. The supply of raw material is just sufficient to produce 1500 toys per day, regardless of their types.
3. The electric switch is only required for type Q toys and is available at a rate of 600 pieces per day.
4. The company can produce any number of toys, as long as it does not exceed the maximum production time or the availability of raw materials and electric switches.
Solution
To maximize profits, we need to determine the optimal production quantities for P and Q toys. Let's break down the problem into smaller steps:
Step 1: Determine the Maximum Production Quantity of Toy Q
Since the production time of Q is twice that of P, we can allocate a certain proportion of the maximum production time to Q. Let's assume that x time units are allocated to P, and 2x time units are allocated to Q.
Step 2: Calculate the Maximum Production Quantity of Toy P
Using the allocated time units, we can determine the maximum production quantity of P by dividing the total available time units (2000) by the production time of P (x).
Step 3: Determine the Maximum Production Quantity of Toy Q
Using the allocated time units, we can determine the maximum production quantity of Q by dividing the total available time units (2000) by the production time of Q (2x).
Step 4: Determine the Maximum Profit
To calculate the maximum profit, we need to consider the following factors:
- The maximum production quantity of P (calculated in Step 2)
- The maximum production quantity of Q (calculated in Step 3)
- The profit per unit of P (Rs. 3)
- The profit per unit of Q (Rs. 5)
The maximum profit can be calculated as follows:
Maximum Profit = (Maximum Production Quantity of P * Profit per unit of P) + (Maximum Production Quantity of Q * Profit per unit of Q)
Step 5: Find the Optimal Production Quantities
To find the optimal production quantities, we need to iterate through different values of x (the allocated time units for P). We can start with x = 1 and increment it until the profit starts to decrease. At that point, we can conclude that the optimal production quantities have been found.
Conclusion
Based on the calculations and analysis, the optimal daily production quantities for P and Q toys to maximize profits are 1000 and 500, respectively.
A company produces two types of toys, P and Q. The production time of Q is twice that of P. The company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys of any type per day. Toy type Q requires an electric switch, which is available at a rate of 600 pieces per day. The company makes a profit of Rs. 3 and Rs. 5 on type P and Q toys, respectively. The task is to determine the daily production quantities of P and Q toys that will maximize the company's profits.
Assumptions
Before proceeding with the solution, let's make some assumptions:
1. The production time required for P and Q toys is measured in time units.
2. The supply of raw material is just sufficient to produce 1500 toys per day, regardless of their types.
3. The electric switch is only required for type Q toys and is available at a rate of 600 pieces per day.
4. The company can produce any number of toys, as long as it does not exceed the maximum production time or the availability of raw materials and electric switches.
Solution
To maximize profits, we need to determine the optimal production quantities for P and Q toys. Let's break down the problem into smaller steps:
Step 1: Determine the Maximum Production Quantity of Toy Q
Since the production time of Q is twice that of P, we can allocate a certain proportion of the maximum production time to Q. Let's assume that x time units are allocated to P, and 2x time units are allocated to Q.
Step 2: Calculate the Maximum Production Quantity of Toy P
Using the allocated time units, we can determine the maximum production quantity of P by dividing the total available time units (2000) by the production time of P (x).
Step 3: Determine the Maximum Production Quantity of Toy Q
Using the allocated time units, we can determine the maximum production quantity of Q by dividing the total available time units (2000) by the production time of Q (2x).
Step 4: Determine the Maximum Profit
To calculate the maximum profit, we need to consider the following factors:
- The maximum production quantity of P (calculated in Step 2)
- The maximum production quantity of Q (calculated in Step 3)
- The profit per unit of P (Rs. 3)
- The profit per unit of Q (Rs. 5)
The maximum profit can be calculated as follows:
Maximum Profit = (Maximum Production Quantity of P * Profit per unit of P) + (Maximum Production Quantity of Q * Profit per unit of Q)
Step 5: Find the Optimal Production Quantities
To find the optimal production quantities, we need to iterate through different values of x (the allocated time units for P). We can start with x = 1 and increment it until the profit starts to decrease. At that point, we can conclude that the optimal production quantities have been found.
Conclusion
Based on the calculations and analysis, the optimal daily production quantities for P and Q toys to maximize profits are 1000 and 500, respectively.
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A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct answer is option 'A'. Can you explain this answer?
Question Description
A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct 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 A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct 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 A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct answer is option 'A'. Can you explain this answer?.
A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct 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 A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct 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 A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct answer is option 'A'. Can you explain this answer?.
Solutions for A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct 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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ample number of questions to practice A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be[2004]a)1000, 500b)800, 600c)500, 1000d)1000, 1000Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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