A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \(Z=5x+7y,\) where x and y are the number of units of X and Y respectively sold. Which of the following statement is correct?
(A)
The objective function maximizes the difference of the profit earned from products X and Y.
(B)
The objective function measures the total production of products X and Y.
(C)
The objective function maximizes the combined profit earned from selling X and Y.
(D)
The objective function ensures the company produces more of product X than product Y.
The objective function maximizes the combined profit earned from selling products X and Y.
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Step-by-Step Solution
The objective function \(Z = 5x + 7y\) represents the total profit earned from selling x units of product X and y units of product Y. The coefficient 5 represents the profit per unit of X, and the coefficient 7 represents the profit per unit of Y.
Option (A) is incorrect because the objective function does not maximize the difference of profits.
Option (B) is incorrect because the objective function measures the total profit, not the total production.
Option (C) is correct because the objective function \(Z = 5x + 7y\) maximizes the combined profit earned from selling products X and Y.
Option (D) is incorrect because the objective function does not ensure the company produces more of product X than product Y; it only represents the profit earned.
Correct Answer: The objective function maximizes the combined profit earned from selling X and Y.
AI Suggestion: Option C
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Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because it requires students to apply their understanding of objective functions in linear programming to interpret the given function and select the correct statement.
Knowledge Dimension:CONCEPTUAL
Justification:The question tests the understanding of the concept of an objective function in the context of linear programming, specifically how it represents profit maximization.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the understanding of the definition and purpose of an objective function, a core concept taught in the textbook.