CP ALG II 10/5/15
3.1 – 3.4 Review
a. Graph.
Name:_______________________________
ì5x + 2y £ -8
ï
í 3x + 4y £ 12
ï8y > x - 32
î
b. Point A is the intersection of boundary lines 3x + 4y £ 12 and 8y > x - 32 . Use
ELIMINATION to find the coordinates of point A.
c.
Point B is the intersection of boundary lines 3x + 4y £ 12 and 5x + 2y £ -8 .
SUBSTITUTION to find the coordinates of point B.
Use
STUGO will screen print t-shirts and sweatshirts to sell during Homecoming week. They have at
most 20 hrs (1200 minutes) to make this apparel and can spend no more than $600 on supplies. To
be worthwhile, they want to have at least 50 items to sell. A t-shirt requires $4 for supplies, takes
only 10 min to print, and has a profit of $6. A sweatshirt requires $20 for supplies, takes 30 min to
print, and has a profit of $20. Make a recommendation that will help STUGO maximize their profit.
What is the maximum possible profit?
a. Define the variables:
b. Write the constraint inequalities in algebraic form:
c. Graph the constraints on the grid below. Label the axes and shade feasible region.
d. Find the coordinates of the vertices that bound the feasible region.
e. Write the objective function.
f. Using the objective function, find the profit from the combinations of T-Shirts and
sweatshirts that you found in part d.
g. What is the combination of t-shirts and sweatshirts that gives the maximum profit
for STUGO? What is the profit for this combination?
Solve this system by ELIMININATION:
3x + 4 y + 5z = 32
4 x + 3y - 6z = -31
5x - 2y + 3z = 30
Create a system of two equations with two variables that has no solution.