The Standard blend of coffee uses 4 oz arabica beans and 12 oz of robusta beans per package; the Deluxe blend uses 10 oz of arabica beans and 6 oz of robusta beans per package. The merchant has 80 lbs. of arabica beans and 90 lbs. of robusta beans available. Find a system of inequalities that describes the possible number of Standard and Deluxe packages the merchant can make.
To find the system of inequalities that describes the possible number of Standard and Deluxe packages the merchant can make, we need to consider two constraints: the available quantity of arabica beans and the available quantity of robusta beans.
Let's assume that the number of Standard packages is represented by "x" and the number of Deluxe packages is represented by "y".
Arabica Beans Constraint:
The Standard blend uses 4 oz of arabica beans per package, and the Deluxe blend uses 10 oz of arabica beans per package. The merchant has 80 lbs. of arabica beans available, which is equivalent to 1280 oz (since 1 lb = 16 oz). So, the inequality to represent the available arabica beans is:
4x + 10y ≤ 1280
Robusta Beans Constraint:
The Standard blend uses 12 oz of robusta beans per package, and the Deluxe blend uses 6 oz of robusta beans per package. The merchant has 90 lbs. of robusta beans available, which is equivalent to 1440 oz. So, the inequality to represent the available robusta beans is:
12x + 6y ≤ 1440
Therefore, the system of inequalities that describes the possible number of Standard and Deluxe packages the merchant can make is:
4x + 10y ≤ 1280
12x + 6y ≤ 1440