End of Chapter 8 Packet
Refer to sections 8.7 and 8.8 in the text book.
Name _____________________________
1.) Consider the system of inequalities:
6 x  8 y  48
0 y4
0 x7
a.) Graph the inequalities.
b.) List the coordinates of the vertices.
c.) Find the maximum and minimum values of the objective function, P  17 x  3 y  60 , and the
values of x and y for which they occur.
2.) A bead store sells necklaces that you make yourself. Customers create jewelry by selecting beads
from various bins. Caroline wants to design her own ETHS necklace from blue and orange beads. She
wants to make a necklace that uses at least 12 total beads but no more than 24 total beads. Caroline
also wants her necklace to contain at least twice as many orange beads as blue beads. Orange beads
cost $2.50 apiece, and blue beads cost $1.50 apiece. Caroline doesn’t want to spend a lot of money for
the necklace.
a.) Define your variables.
b.) Write the constraints. (There are 5)
c.) Graph the feasible region.
d.) Write the objective function.
e.) Find the corner points, and use them to find the optimal solution.
3.) Dovetail Carpentry Shop makes bookcases and desks. Each bookcase requires 5 hours of
woodworking and 4 hours of finishing. Each desk requires 10 hours of woodworking and 3 hours of
finishing. Each month the shop has 600 hours of labor available for woodworking and 240 hours for
finishing. The profit on each bookcase is $40 and on each desk is $75. How many of each product
should be made each month in order to maximize profit?
4.) To prevent traffic jams, a city funds a courtesy patrol to aid stranded drivers on local roads. The
patrol can repair a flat tire, provide the motorist with 2 gallons of gas, or call a tow truck for more serious
problems. It takes 15 minutes to help a driver who is out of gas and 45 minutes to help a driver with a
flat tire. The courtesy patrol driver carries 28 gallons of gas. What is the maximum number of stops for
flat tires or empty gas tanks that the courtesy patrol can make in an 8-hour shift?
a.) Define your variables.
b.) Write the constraints. (Hint: There are 4)
c.) Write the objective function.
5.) Dr.Carter’s dental practice is open for 7 hours each day. Her receptionist schedules appointments,
allowing ½ hour for a cleaning and 1 hour to fill a cavity. She charges $40 for a cleaning and $95 for a
filling. Dr. Carter cannot do more than 4 fillings per day. Find the number of each type of
appointment that maximizes Dr. Carter’s income for the day.
a.) Define your variables.
b.) Write the constraints. (Hint: There are 4)
c.) Write the objective function.
Decompose into partial fractions:
6.)
51x  19
6 x  37 x  35
7.)
13x  46
12 x 2  11x  15
2
8.)
9.)
10 x3  15 x 2  35 x
x2  x  6
4 x 2  2 x  10
 3x  5 x  1
2