Understanding Linear Inequalities in Budget Constraints

Medium Heart Of Algebra Linear Equations And Inequalities

Consider a linear inequality that represents a budget constraint for a small business. The inequality is given by:

$$3x + 5y \leq 30$$

where x is the number of product A produced and y is the number of product B produced. What does this inequality indicate about the possible combinations of product A and product B the business can produce, if the business decides to maximize its production while not exceeding the budget?

The business can produce any positive integer values for x and y.

The business can produce only combinations where either x is 0 or y is 0.

The business can produce combinations of A and B such that the total cost does not exceed $30.

The business must produce more of product A than product B.

Hint

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