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A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500?
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A company earns profit of Rs 250 and Rs 375 per unit on product X and ...
Solution:
Objective function: Maximize profit = 250x + 375y
Constraints:
4x + 2y ≤ 25,000
3x + 2y ≤ 20,000
where x and y are the number of units of product X and Y respectively.
To solve this problem, we need to use the graphical method.
Step 1: Find the intercepts of the two constraints.
4x + 2y = 25,000
When x = 0, y = 12,500
When y = 0, x = 6,250
3x + 2y = 20,000
When x = 0, y = 10,000
When y = 0, x = 6,666.67
Step 2: Plot the intercepts on a graph and draw the lines.
Step 3: Shade the feasible region.
The feasible region is the region that satisfies all the constraints. In this case, it is the region below both lines and within the positive quadrant.
Step 4: Find the corner points of the feasible region.
The corner points of the feasible region are (0, 0), (6,250, 0), (4,166.67, 4,166.67), and (0, 10,000).
Step 5: Calculate the profit at each corner point.
(0, 0) Profit = 0
(6,250, 0) Profit = 1,562,500
(4,166.67, 4,166.67) Profit = 2,604,167
(0, 10,000) Profit = 3,750,000
Step 6: Choose the corner point with the maximum profit.
Therefore, the maximum profit that the company could earn subject to the given constraints is Rs 3,750,000.
Answer: c) Rs 3,750,000
Objective function: Maximize profit = 250x + 375y
Constraints:
4x + 2y ≤ 25,000
3x + 2y ≤ 20,000
where x and y are the number of units of product X and Y respectively.
To solve this problem, we need to use the graphical method.
Step 1: Find the intercepts of the two constraints.
4x + 2y = 25,000
When x = 0, y = 12,500
When y = 0, x = 6,250
3x + 2y = 20,000
When x = 0, y = 10,000
When y = 0, x = 6,666.67
Step 2: Plot the intercepts on a graph and draw the lines.
Step 3: Shade the feasible region.
The feasible region is the region that satisfies all the constraints. In this case, it is the region below both lines and within the positive quadrant.
Step 4: Find the corner points of the feasible region.
The corner points of the feasible region are (0, 0), (6,250, 0), (4,166.67, 4,166.67), and (0, 10,000).
Step 5: Calculate the profit at each corner point.
(0, 0) Profit = 0
(6,250, 0) Profit = 1,562,500
(4,166.67, 4,166.67) Profit = 2,604,167
(0, 10,000) Profit = 3,750,000
Step 6: Choose the corner point with the maximum profit.
Therefore, the maximum profit that the company could earn subject to the given constraints is Rs 3,750,000.
Answer: c) Rs 3,750,000
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A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500?
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A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500?.
A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500?.
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A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500?, a detailed solution for A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500? has been provided alongside types of A company earns profit of Rs 250 and Rs 375 per unit on product X and Y respectively. 68) Find the maximum profit that the company could earn if the company is subject to the following constraints: 4x 2y ≤ 25,000 3x 2y ≤ 20,000 a) Rs 1,666,667 b) Rs 2,187,500 c) Rs 3,750,000 d) Rs 4,687,500? theory, EduRev gives you an
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