Name:__________________________________________
Practice With Linear Programming: Real-World Modeling
PROBLEM #1
You are going to make and sell bread two types of bread, Irish soda bread and Kugelhopf cake. A
loaf of Irish soda bread is made with 2 c flour and ¼ c sugar. Kugelhopf cake is made with 4 c of
flour and 1 c sugar. Let x denote the amount of Irish soda bread, and let y denote the amount of
Kugelhopf cake.
1. What constraint must be satisfied if you only have 16 c of flour to use?
2. What constraint must be satisfied if you only have 3 c of sugar to use?
3. What additional constraints must be satisfied because the problem involves real objects?
4. Graph the constraints on the grid and label its vertices. Call the vertex on the x-axis A, the
vertex on the y-axis B, and the vertex on neither axis C. Label the origin O. Find the coordinates
of each vertex.
Vertices
Coordinates:
A
B
C
O
5. Suppose that you will make a $1.50 profit on each loaf of Irish soda bread and a profit of $4 on
each Kugelhopf cake.
a. What is the objective function?
b. What is the value of the objective function on vertex A?
c. At vertex B?
d. At vertex C
e. What combination of Irish soda bread and Kugelhopf cake should you make in order to
maximize your profit? What will your maximum profit be?