Worksheet 3-3
Advanced Algebra & Trigonometry
Name ___________________________________
Block __________
Directions: Graph each system of inequalities. Name the coordinates of the vertices of
the feasible region. Find the max and min values of the given function for this
region.
1. x  1
y6
y  x2
f  x, y   x  y
2. x  1
y6
y  x2
f  x, y   x  y
3. x  1
xy 6
f  x, y   x  2 y
4. y  2 x
y 6x
y6
f  x, y   4 x  3 y
5. y   x  2
y  3x  2
y  x4
f  x , y   3 x  5 y
6. y  3 x  6
4y  3 x  3
x  2
f  x, y    x  3 y
Directions: Solve the Optimization problems. Be sure to follow the steps!!
7. A backpack manufacturer produces an internal frame pack and an external
frame pack. Let x represent the number of internal frame backpacks sold in an
hour and let y represent the number of external frame backpacks sold in an hour.
Then the inequalities x  3y  18 , 2 x  y  16 , x  0 , and y  0 describe the
constraints for manufacturing both packs. Use the profit function:
f(x, y) = 50x + 80y and the constraints given to determine the maximum profit for
manufacturing both backpacks for the given constraints.
8. Jenny’s bakery makes two types of birthday cakes: yellow cake which sells for
$25, and strawberry cake, which sells for $35. Both cakes are the same size, but
the decorating and assembly time require for the yellow cake is 2 hours, while the
time is 3 hours for the strawberry cake. There are 450 hours of labor available for
production. How many of each type of cake should be made to maximize
revenue?
Step 1:
Step 2:
Step 5:
Step 6: