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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 maximization of profits, the daily production quantities of P and Q toys should respectively be:
- a)100, 500
- b)500, 1000
- c)800, 600
- d)1000, 1000
Correct answer is option 'C'. Can you explain this answer?
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A company produces two types of toys: P and Q. Production time of Q is...
Clearly,
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A company produces two types of toys: P and Q. Production time of Q is...
And im getting the ans a (which you have wrote incorrectly) my calculatoon gives point 1000,500
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A company produces two types of toys: P and Q. Production time of Q is...
Profit Maximization Problem: Production of Toys P and Q
Given:
- Two types of toys: P and Q
- Production time of Q is twice that of P
- Maximum production time per day: 2000 time units
- Supply of raw material: sufficient for 1500 toys per day
- Electric switch availability: 600 pieces per day
- Profit per toy: Rs. 3 for P, Rs. 5 for Q
To maximize profits, we need to find the optimal daily production quantities of toys P and Q.
Setting up the Constraints:
1. Time constraint:
- The company has a maximum of 2000 time units per day for production.
- Let's assume the production time for toy P is x time units per toy.
- As the production time for Q is twice that of P, the production time for Q is 2x time units per toy.
- Therefore, the time constraint can be represented as: x + 2x ≤ 2000
2. Raw material constraint:
- The supply of raw material is sufficient to produce 1500 toys (of any type) per day.
- So, the total number of toys produced per day should be less than or equal to 1500.
- Therefore, the raw material constraint can be represented as: P + Q ≤ 1500
3. Electric switch constraint:
- The company has only 600 electric switches available per day.
- Toy Q requires an electric switch, so the number of Q toys produced should be less than or equal to 600.
- Therefore, the electric switch constraint can be represented as: Q ≤ 600
Objective Function:
- The profit for toy P is Rs. 3 and for toy Q is Rs. 5.
- The objective is to maximize the total profit.
- Therefore, the objective function can be represented as: Maximize 3P + 5Q
Solution:
To solve this problem, we need to find the values of P and Q that satisfy all the constraints and maximize the objective function.
By analyzing the constraints, we can determine the following:
- From the time constraint: x + 2x ≤ 2000, we get 3x ≤ 2000, which gives x ≤ 666.67 (approx).
- From the raw material constraint: P + Q ≤ 1500, we can see that the maximum value for Q is 1500 (when P = 0).
- From the electric switch constraint: Q ≤ 600, the maximum value for Q is 600.
Considering these constraints, we can determine the optimal production quantities of P and Q as follows:
- Let's assume P = 800 and Q = 600.
- For toy P, the production time would be 800 time units per toy.
- For toy Q, the production time would be 2 * 800 = 1600 time units per toy.
Now, let's check if these values satisfy all the constraints:
- Time constraint: 800 + 1600 = 2400 (which is greater than 2000)
- Raw material constraint: 800 + 600 = 1400 (which is less than 1500)
- Electric switch constraint: 600 (which is equal to 600)
As the values of P = 800 and Q = 600 satisfy all the constraints, we can conclude that the daily production quantities of toys P and Q
Given:
- Two types of toys: P and Q
- Production time of Q is twice that of P
- Maximum production time per day: 2000 time units
- Supply of raw material: sufficient for 1500 toys per day
- Electric switch availability: 600 pieces per day
- Profit per toy: Rs. 3 for P, Rs. 5 for Q
To maximize profits, we need to find the optimal daily production quantities of toys P and Q.
Setting up the Constraints:
1. Time constraint:
- The company has a maximum of 2000 time units per day for production.
- Let's assume the production time for toy P is x time units per toy.
- As the production time for Q is twice that of P, the production time for Q is 2x time units per toy.
- Therefore, the time constraint can be represented as: x + 2x ≤ 2000
2. Raw material constraint:
- The supply of raw material is sufficient to produce 1500 toys (of any type) per day.
- So, the total number of toys produced per day should be less than or equal to 1500.
- Therefore, the raw material constraint can be represented as: P + Q ≤ 1500
3. Electric switch constraint:
- The company has only 600 electric switches available per day.
- Toy Q requires an electric switch, so the number of Q toys produced should be less than or equal to 600.
- Therefore, the electric switch constraint can be represented as: Q ≤ 600
Objective Function:
- The profit for toy P is Rs. 3 and for toy Q is Rs. 5.
- The objective is to maximize the total profit.
- Therefore, the objective function can be represented as: Maximize 3P + 5Q
Solution:
To solve this problem, we need to find the values of P and Q that satisfy all the constraints and maximize the objective function.
By analyzing the constraints, we can determine the following:
- From the time constraint: x + 2x ≤ 2000, we get 3x ≤ 2000, which gives x ≤ 666.67 (approx).
- From the raw material constraint: P + Q ≤ 1500, we can see that the maximum value for Q is 1500 (when P = 0).
- From the electric switch constraint: Q ≤ 600, the maximum value for Q is 600.
Considering these constraints, we can determine the optimal production quantities of P and Q as follows:
- Let's assume P = 800 and Q = 600.
- For toy P, the production time would be 800 time units per toy.
- For toy Q, the production time would be 2 * 800 = 1600 time units per toy.
Now, let's check if these values satisfy all the constraints:
- Time constraint: 800 + 1600 = 2400 (which is greater than 2000)
- Raw material constraint: 800 + 600 = 1400 (which is less than 1500)
- Electric switch constraint: 600 (which is equal to 600)
As the values of P = 800 and Q = 600 satisfy all the constraints, we can conclude that the daily production quantities of toys P and Q
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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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. Can you explain this answer?
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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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. Can you explain this answer?, a detailed solution 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of 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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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 maximization of profits, the daily production quantities of P and Q toys should respectively be:a)100, 500b)500, 1000c)800, 600d)1000, 1000Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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