Math 141 Week in Review
Week 4 Problem Set Answers
For all graphs, please see the WIR solutions file.
1.
A. Corner Points: (0, 1), (0, 4), (3, 2), ( 2.5, 1); Feasible region is bounded.
B. Corner Points: (2, 1), (3, 6), (5, 4), (5, 2); Feasible region is bounded.
2.
Corner Points: (0, 16), (2, 4), (4, 2), (16, 0); (Feasible region is unbounded)
C is minimized at (2, 4) with a minimum value of 22.
Follow up question: C has no maximum.
3.
Corner Points: (3, 8), (8, 10), (12, 2)
The maximum value of P is 260 and is attained at infinitely points, which lie on
the line segment joining the points (8, 10) and (12, 2).
4.
Let x = $ amount invested in bonds.
Let y = $ amount invested in savings account.
Maximize I = 0.05x + 0.09y
Subject to:
x + y ! 60000
y " 10000
x " 2y
x "0
y "0
5.
Let x = amount of time spent walking
Let y = amount of time spent navigating the boat
Minimize E = 300x + 230y
Subject to:
3x + 12y ! 240
x + y " 48
y " 18
x !0
y !0
6.
Let x = the number of times program A is aired each week.
Let y = the number of times program B is aired each week.
Maximize L = 100000x + 30000y
Subject to:
20x + 10y ! 80
x+ y "6
x "0
y "0
Corner Points: (0, 6), (0, 8), (2, 4)
The number of listeners is maximized when they air 2 program A’s and 4 program
B’s in a week. The maximum number of listeners is 320,000.
7.
A. Let x = the number of bags of Morning Blend made each day.
Let y = the number of bags of Wired Blend made each day.
Minimize C = 4x + 6y
Subject to:
x + 2y !120
2x + y !150
x + y " 24
x "0
y "0
Corner Points: (24, 0), (75, 0), (0, 24), (0, 60), (60, 30)
The cost is a minimum of $96 when 24 bags of Morning Blend and 0 bags of
Wired Blend are mixed each day.
B. There are 96 pounds of Sumatran coffee beans and 102 pounds of Colombian
beans left over.