Download Date Period - Godley ISD

Name ________________________________ Date __________________ Period ______
Review # 3 – Graphing Inequalities
Graph.
1. x – y < 4
2. 2x + 5y < -10
Solve the following system of inequalities.
3. x – 2y < -4
x + 2y > 4
y< 4
Review # 3
4. 2x + y > –6
x–y > 4
5x + y < 10
Find the maximum value and the minimum value of P under the constraints. Find the corners
and SHOW ALL WORK.
5. P = 4x – 3y
Constraints:
x  1
y>2
x + y  10
x – y > -4
List Vertices (corners):
1.
P1 = __________
2.
P2 = __________
3.
P3 = __________
4.
P4 = __________
The maximum value of P is ______ when x = ______ and y = ______.
The minimum value of P is ______ when x = ______ and y = ______.
Review # 3
Use linear programming to solve the following problem (numbers 6 – 10).
6. You are the manager of a store that sells home computers. You are getting ready to order
next month’s stock and are trying to decide how many of each of two models of monitors to order
to maintain a maximum profit. The profit is $45 on monitor Model A and $50 on monitor model B.
Let x = the number of monitor Model A you order
Let y = the number of monitor Model B you order
Constraints:
Model A will cost you $250 and model B will cost
you $400 to order. You do not want to order more
than $70,000 worth of the two models.
Inequalities
______________________
x-int_______ y-int_______
Your combined sales of Models A and B will
not exceed 250 units.
_____________________
x-int_______ y-int_______
They must have at least 24 of each model in stock.
(Assume they are currently out of stock on each.)
_______________
________________
Write the equation which represents the amount of profit from the sales of both models.
P = ______________________________
7. Sketch the graph of the constraint
inequalities and label the vertices of #6.
Review # 3
8. What are the corners of #7?
____________
____________
____________
____________
9. What is the calculated profit for each of the vertices? (show work for all)
10. What is the Maximum profit? ___________ How many of each kind needs to be ordered?
_________________ of Model A and ________________of Model B
Use linear programming to solve the following problem (numbers 11 – 15).
11. The Pottery Shop makes two kinds of birdbaths: unglazed and glazed. The shop’s profit on
each unglazed birdbath is $10.00, while its profit on the glazed birdbath is $15.00.
Let x = the number of unglazed birdbaths
Let y = the number of glazed birdbaths
Constraints:
The unglazed birdbath requires 1 hour to
throw on the wheel and the glazed birdbath
takes 2 hours on the wheel. The wheel is
available at most 80 hours per week.
The unglazed must be in the kiln for 2 hours
and the glazed requires 6 hours in the kiln.
The kiln is available at most 180 hours per week.
Inequalities
______________________
x-int_______ y-int_______
_____________________
x-int_______ y-int_______
Write the equation which represents the amount of profit from the sales of both models.
P = ______________________________
Review # 3
COPY from #11.
Constraint #1: Ineq:__________________
x-intercept___________ y-intercept___________
Constraint #2: Ineq:__________________
x-intercept___________ y-intercept___________
P = __________________________
12. Sketch the graph of the constraint
inequalities and label the vertices.
13. What are the corners?
____________
____________
____________
____________
14. What is the calculated profit for each of the vertices? (show work for all)
15. What is the Maximum profit? ___________ How many of each kind needs to be made?
_________________ unglazed birdbaths and ________________glazed birdbaths
Review # 3
Review.
16. Solve
3
(4x – 8) + (2x – 3) = 1
4
__________________
17. Write the equation that represents the data.
x
-5
-1
3
5
9
y
-22
-10
2
8
20
_________________
18. Gloria has some change in her wallet that is made up of nickels and dimes. There are 4
more nickels than dimes. The value of the coins is $2.60. Using a system of equations, find the
number of nickels Gloria has in her wallet.
_________________
Answers
1.
13. Corners: (0, 30),
(60, 10), (80, 0),
(0, 0)
5.
14. P(0, 30) = $450
P(0, 0) = $0
P(60, 10) = $750)
P(80, 0) = $800
15. Max profit is $800…
…80 unglazed birdbaths
and 0 glazed birdbaths
2.
Max=26,x=8,y=2
Min=-11,x=1,y=5
16. x = 2
17. y = 3x – 7
6. 250x + 400y ≤ 70,000 ;
(280, 0) and (0, 175)
x + y ≤ 250 ;
(250, 0) and (0, 250)
x ≥ 24
y ≥ 24
P = 45x + 50y
3.
7. Graph depends upon
scale used – see worked key
for example
8. Corners: (24, 24),
(24, 160), (200, 50)
(226, 24)
4.
9. P(24, 24) = $2280
P(24, 160) = $9080
P(200, 50) = $11,500
P(226, 24) = $11,370
10. Max profit is $11,500…
… order 200 of Model A
and 50 of Model B
11. x + 2y ≤ 80 ;
(80, 0) and (0, 40)
2x + 6y ≤ 180 ;
(90, 0) and (0, 30)
P = 10x + 15y
12. Graph depends upon
scale used – see worked key
for example
18. 20 nickels