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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)1000, 500
- b)500, 100
- c)800, 600
- 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...
Solve this problem, by the linear programming model.
View all questions of this test
We have to make the constraints from the given conditions.
For production conditions
P + 2Q < />
For raw material
P+Q< />
For electric switch
Q< />
For maximization of profit, objective function
Z = 3P+5Q ......(iV)
From the equations (i), (ii) & (iii), draw a graph for toy P and Q
Line (i) and line (ii) intersects at point A, we have to calculate the intersection point.
P + 2Q = 2000
P + Q = 1500
After solving there equations, we get A(1000, 500)
For point B,
P + 2Q = 2000
Q = 600
P = 2000 - 1200 = 800
So, B(800,600)
Here shaded area shows the area bounded by the three line equations (common area)
This shaded area have five vertices.
So, for maximization of profit
P = 1000 from point (ii)
Q = 500
Most Upvoted Answer
A company produces two types of toys: P and Q. Production time of Q i...
Given Constraints:
- Production time of Q is twice that of P
- Maximum of 2000 time units per day
- Raw material supply for 1500 toys per day
- Electric switch for Q available @ 600 pieces per day
Profit per Toy:
- Profit on type P = Rs.3
- Profit on type Q = Rs.5
Maximizing Profits:
To maximize profits, we need to consider the constraints given and calculate the optimal production quantities for types P and Q.
Calculating Production Quantities:
Let the daily production quantities of P and Q toys be x and y respectively.
Constraints:
- Production time constraint: 2x + y ≤ 2000
- Raw material supply constraint: x + y ≤ 1500
- Electric switch constraint: y ≤ 600
Profit Maximization:
Maximize Z = 3x + 5y
Solving the Linear Programming Problem:
By solving the above constraints and maximizing the profit function Z, we get:
x = 1000, y = 500
Therefore, the daily production quantities of P and Q toys should be 1000 and 500 respectively to maximize profits.
- Production time of Q is twice that of P
- Maximum of 2000 time units per day
- Raw material supply for 1500 toys per day
- Electric switch for Q available @ 600 pieces per day
Profit per Toy:
- Profit on type P = Rs.3
- Profit on type Q = Rs.5
Maximizing Profits:
To maximize profits, we need to consider the constraints given and calculate the optimal production quantities for types P and Q.
Calculating Production Quantities:
Let the daily production quantities of P and Q toys be x and y respectively.
Constraints:
- Production time constraint: 2x + y ≤ 2000
- Raw material supply constraint: x + y ≤ 1500
- Electric switch constraint: y ≤ 600
Profit Maximization:
Maximize Z = 3x + 5y
Solving the Linear Programming Problem:
By solving the above constraints and maximizing the profit function Z, we get:
x = 1000, y = 500
Therefore, the daily production quantities of P and Q toys should be 1000 and 500 respectively to maximize profits.
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Community Answer
A company produces two types of toys: P and Q. Production time of Q i...
Solve this problem, by the linear programming model.
We have to make the constraints from the given conditions.
For production conditions
P + 2Q < />
For raw material
P+Q< />
For electric switch
Q< />
For maximization of profit, objective function
Z = 3P+5Q ......(iV)
From the equations (i), (ii) & (iii), draw a graph for toy P and Q
Line (i) and line (ii) intersects at point A, we have to calculate the intersection point.
P + 2Q = 2000
P + Q = 1500
After solving there equations, we get A(1000, 500)
For point B,
P + 2Q = 2000
Q = 600
P = 2000 - 1200 = 800
So, B(800,600)
Here shaded area shows the area bounded by the three line equations (common area)
This shaded area have five vertices.
So, for maximization of profit
P = 1000 from point (ii)
Q = 500
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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)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. 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)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 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)1000, 500b)500, 100c)800, 600d)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 maximization of profits, the daily production quantities of P and Q toys should respectively be?a)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 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)1000, 500b)500, 100c)800, 600d)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 maximization of profits, the daily production quantities of P and Q toys should respectively be?a)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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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 maximization of profits, the daily production quantities of P and Q toys should respectively be?a)1000, 500b)500, 100c)800, 600d)1000, 1000Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
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