This problem can be solved using linear programming. Let's define the variables and constraints to maximize the profit.

Step 1: Define Variables

Let:

• $x$ be the number of economy blend packages produced.
• $y$ be the number of superior blend packages produced.

Step 2: Define the Coffee Usage in Each Blend

Each economy blend package uses:

• 2 ounces of A grade coffee.
• 10 ounces of B grade coffee.

Each superior blend package uses:

• 9 ounces of A grade coffee.
• 2 ounces of B grade coffee.

Step 3: Constraints (Coffee Availability)

• The total amount of A grade coffee available is 1,728 ounces.
• The total amount of B grade coffee available is 1,760 ounces.

We can express these as:

1. A grade coffee constraint: $2x + 9y \leq 1728$ (Total ounces of A grade coffee used by economy and superior blend packages must be less than or equal to 1,728 ounces.)

2. B grade coffee constraint: $10x + 2y \leq 1760$ (Total ounces of B grade coffee used by economy and superior blend packages must be less than or equal to 1,760 ounces.)

Step 4: Objective Function (Profit Maximization)

The profit per economy blend is $3, and the profit per superior blend is $4. The objective is to maximize the total profit: $\text{Maximize } 3x + 4y$

Step 5: Non-negativity Constraints

Both $x$ and $y$ must be non-negative: $x \geq 0, \quad y \geq 0$

Step 6: Solve the System

We need to solve the system of inequalities: