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Math 141 WIR, Spring 2007, Benjamin
Aurispa
Math 141 Week-in-Review 4 Answer Key
Note: To see graphs corresponding to these problems, please see the full solutions from the live
Week-in-Review.
1. (a) Corner Points: (0, 1), (0, 4), (3, 2), ( 25 , 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 bond.
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 = pounds of food I.
Let y = pounds of food II.
Minimize C = 0.20x + 0.15y
Subject to:
100x + 10y ≥ 260
40x + 80y ≥ 320
10x + 5y ≥ 50
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.
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c
Math 141 WIR, Spring 2007, Benjamin
Aurispa
7. On the following problem, the answer to the way I had the problem originally written was for
them to make 0 bags of each type of coffee for a minimum cost of $0. This is a trivial answer,
so during the week in review, I added the conditions that they must make at least one bag of
each type of coffee. Although the answer is still unrealistic, it does illustrate leftover resources,
which was the point.
(a) Let x = the number of bags of Morning Blend made each day.
Let y = the number of bags of South American Blend made each day.
Minimize C = 4x + 2y
Subject to:
2x + y ≤ 300
x + 2y ≤ 240
x≥1
y≥1
Corner Points: (1, 1), (1, 239
), (120, 60), ( 299
, 0)
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The cost is minimized when 1 bag of Morning Blend and 1 bag of South American Blend
are made each day. The minimum cost is $6.
(b) There are 297 pounds of Mexican coffee beans left over and 237 pound of Colombian beans
left over.
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