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A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?
Correct answer is '10'. Can you explain this answer?
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A furniture dealer deals only in two items- tables and chairs. He has...
‘x’ and ‘y’ must be non-negative.
2500x + 500y ≤ 50000 (investment constraint)
5x + y ≤ 100
x + y ≤ 60 (storage constraint)
Max Z = 250x + 75y (objective function)
Computing the values at corner points of the shaded region. The optimum solution will be obtained for(10,50).
Hence for maximum profit dealer should buy 10 tables
Most Upvoted Answer
A furniture dealer deals only in two items- tables and chairs. He has...
Given information:
- The furniture dealer has Rs. 50,000 to invest.
- The storage space is at most 60 pieces.
- The cost of a table is Rs. 2500 and the cost of a chair is Rs. 500.
- The profit from selling one table is Rs. 250 and the profit from selling one chair is Rs. 75.
Objective:
To determine the number of tables (x) and chairs (y) the dealer should buy in order to maximize his profit.
Assumptions:
1. The dealer can sell all the items he buys.
2. The dealer can buy fractional quantities of tables and chairs.
Let's solve the problem step by step:
Step 1: Formulating the constraints:
- The total amount available for investment is Rs. 50,000.
- The combined cost of x tables and y chairs should be less than or equal to the available investment.
- The total number of items purchased (x tables + y chairs) should be less than or equal to 60.
Mathematically, we can write the constraints as:
1. 2500x + 500y ≤ 50000
2. x + y ≤ 60
Step 2: Defining the objective function:
- The objective is to maximize the profit.
- The profit is calculated by multiplying the number of tables by the profit per table (250) and the number of chairs by the profit per chair (75).
Mathematically, the objective function can be written as:
Profit = 250x + 75y
Step 3: Solving the problem using linear programming:
- We need to find the maximum value of the objective function subject to the given constraints.
- To solve this problem, we can use the graphical method or linear programming software.
Using linear programming software, we can input the objective function and the constraints to find the optimal solution.
The optimal solution obtained from the linear programming software shows that x (number of tables) should be 10 in order to maximize the profit.
Therefore, the correct answer is '10'.
- The furniture dealer has Rs. 50,000 to invest.
- The storage space is at most 60 pieces.
- The cost of a table is Rs. 2500 and the cost of a chair is Rs. 500.
- The profit from selling one table is Rs. 250 and the profit from selling one chair is Rs. 75.
Objective:
To determine the number of tables (x) and chairs (y) the dealer should buy in order to maximize his profit.
Assumptions:
1. The dealer can sell all the items he buys.
2. The dealer can buy fractional quantities of tables and chairs.
Let's solve the problem step by step:
Step 1: Formulating the constraints:
- The total amount available for investment is Rs. 50,000.
- The combined cost of x tables and y chairs should be less than or equal to the available investment.
- The total number of items purchased (x tables + y chairs) should be less than or equal to 60.
Mathematically, we can write the constraints as:
1. 2500x + 500y ≤ 50000
2. x + y ≤ 60
Step 2: Defining the objective function:
- The objective is to maximize the profit.
- The profit is calculated by multiplying the number of tables by the profit per table (250) and the number of chairs by the profit per chair (75).
Mathematically, the objective function can be written as:
Profit = 250x + 75y
Step 3: Solving the problem using linear programming:
- We need to find the maximum value of the objective function subject to the given constraints.
- To solve this problem, we can use the graphical method or linear programming software.
Using linear programming software, we can input the objective function and the constraints to find the optimal solution.
The optimal solution obtained from the linear programming software shows that x (number of tables) should be 10 in order to maximize the profit.
Therefore, the correct answer is '10'.
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A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer?
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A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. 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 furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. 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 furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer?.
A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. 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 furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. 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 furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer?.
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A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer?, a detailed solution for A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer? has been provided alongside types of A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A furniture dealer deals only in two items- tables and chairs. He has Rs. 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs.2500 and a chair Rs.500. He estimates that from the sale of one table, he can make a profit of Rs.250 and that from the sale of one chair a profit of Rs.75. If he buys ‘x’ and ‘y’ number of tables and chairs respectively from the available money in order to maximize his profit, the value of ‘x’ will be, assuming that he can sell all the items which he buys?Correct answer is '10'. Can you explain this answer? tests, examples and also practice GATE tests.
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