Deluxe coffee is to be mixed with regular coffee to make at least 55 pounds of a blended coffee. The mixture must contain at least 11 pounds of deluxe coffee. Deluxe coffee costs $\$ 5$ per pound and regular coffee $\$ 4$ per pound. How many pounds of each kind of coffee should be used to minimize costs? To attain the minimum cost, use coffee. pounds of deluxe coffee and pounds of regular

Step 1 ：We are given that deluxe coffee costs $5 per pound and regular coffee costs $4 per pound. We need to mix these two types of coffee to make at least 55 pounds of a blended coffee, which must contain at least 11 pounds of deluxe coffee. The goal is to minimize the total cost.

Step 2 ：We can solve this problem using linear programming. The decision variables are the number of pounds of deluxe coffee (x) and the number of pounds of regular coffee (y). The objective function is the total cost of the coffee, which is \(5x + 4y\). The constraints are \(x + y \geq 55\) (the total weight of the coffee is at least 55 pounds) and \(x \geq 11\) (the weight of the deluxe coffee is at least 11 pounds).

Step 3 ：The result from the linear programming optimization shows that to minimize the cost, we should use 0 pounds of deluxe coffee and 55 pounds of regular coffee. However, this violates the constraint that we need at least 11 pounds of deluxe coffee.

Step 4 ：Therefore, we need to adjust the result to meet this constraint. We can do this by using 11 pounds of deluxe coffee and reducing the amount of regular coffee by 11 pounds to 44 pounds. This will still meet the total weight constraint of at least 55 pounds.

Step 5 ：Final Answer: To minimize the cost, we should use \(\boxed{11}\) pounds of deluxe coffee and \(\boxed{44}\) pounds of regular coffee.