Name: _____________________________________________________
Practice With Linear Programming: Real-World Modeling
PROBLEM #2
Suppose you make and sell skin lotion. A quart of regular skin lotion contains 2 c of oil and 1 c of
cocoa butter. A quart of extra-rich skin lotion contains 1 c of oil and 2 c of cocoa butter. Let x
denote the amount of regular skin lotion you make, and let y denote the amount of extra-rich cocoa
butter you make.
1. What constraint must be satisfied if you only have 24 c of oil to use?
2. What constraint must be satisfied if you only have 18 c of cocoa butter 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.
Vertices:
A
B
C
O
Coordinates:
5. Suppose that you will make a profit of $10/qt on regular lotion and a profit of $8/qt on extrarich lotion.
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 regular skin lotion and extra-rich skin lotion should you make in
order to maximize your profit? What will your maximum profit be?