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 statements 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.

Hint:

The objective function in linear programming typically represents a quantity to be maximized or minimized, such as profit, cost, or production.

Answer 1

The Correct Option is C

The objective function \( Z = 5x + 7y \) represents the total profit earned by selling \( x \) units of product X and \( y \) units of product Y. The coefficients 5 and 7 indicate the profit per unit of X and Y respectively. Therefore, the function maximizes the combined profit earned from selling both products, as the objective is to maximize \( Z \).