Chapter 8.7, Problem 59AE

Blending Coffee Bill’s Coffee House, a store that specializes in coffee, has available 75 pounds (lb) of $A$ grade coffee and 120 lb of $B$ grade coffee. These will be blended into 1-lb packages as follows: an economy blend that contains 4 ounces (oz) of $A$ grade coffee and 12 oz of $B$ grade coffee, and a superior blend that contains 8 oz of $A$ grade coffee and 8 oz of $B$ grade coffee.

a. Using $x$ to denote the number of packages of the economy blend and $y$ to denote the number of packages of the superior blend, write a system of linear inequalities that describes the possible numbers of packages of each kind of blend.

b. Graph the system and label the corner points.