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 from selling \( x \) units of product X and \( y \) units of product Y. Analysis of the statements follows:

• Statement 1: The function does not maximize the difference of profits; it is a sum of combined profits.
• Statement 2: The function does not measure total production; the coefficients 5 and 7 represent profit contributions, not quantities.
• Statement 3: The function maximizes the combined profit from X and Y, as it sums the total earnings from both products.
• Statement 4: The function does not indicate that more of X than Y is produced, as it lacks constraints on the relationship between \( x \) and \( y \).

Therefore, the correct statement is: The objective function maximizes the combined profit earned from selling X and Y.