CBSE 2025, Set 2

Question

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.

Edvaya · Accepted Answer

The correct answer is The objective function maximizes the combined profit earned from selling X and Y.. **Solution:**

In a Linear Programming Problem (LPP), the objective function is the mathematical equation that represents the primary goal of the system, which is to be either maximized or minimized.

Given the function $Z = 5x + 7y$:
* $x$ and $y$ represent the quantities of products sold.
* $5$ and $7$ represent the unit profit from product X and product Y, respectively.
* The sum $5x + 7y$ calculates the **total combined profit** generated by selling both products.

In business contexts, a profit function is modeled with the goal of maximizing it. Therefore, the objective function represents maximizing the combined profit earned from selling products X and Y.

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Mathematics > Vectors And Linear Programming > Linear Programming

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