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- From: Mathematics, Algebra
- Posted on: Fri 22 Jan, 2016
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1. Solve the linear programming problem.
Maximize and minimize
Z=3x+4y
Subject to 2x + y ? 30
X+2y? 24
X, y ? 0
What is the maximum value of z?
Select the correct choice below and fill in any answer boxes present in your choice.
a. Z=___ (type an integer or a fraction)
b. There is no maximum value of z
What are the coordinates of the corner point where the maximum value of z occurs?
a. Coordinates are___ (type an ordered pair)
b. There is no maximum value of z
What is the minimum value of z?
a. Z= 60
b. There is no minimum value of z
What are the coordinates of the corner point where the minimum value of z occurs?
a. The coordinates are (12, 6)
b. There is no minimum value of z
2. Solve the linear programming problem
Maximize
P=30x+40y
Subject to 2x+y?14
X+ y?9
X + 2y ?16
X, y ?0
What is the maximum value of P?
a. P= 340
b. There is no maximum value of p
What are the coordinates of the corner point where the maximum value of P occurs?
a. The coordinates are (2, 7)
b. There is no maximum value of P
3. A manufacturing company makes two types of water skis, a trick ski, and a slalom ski. The relevant manufacturing data are given in the table.
Labor hours per ski Labor hours per ski Maximum labor hours
Available per day
Department Trick ski Slalom ski
Fabricating 6 4 108
finishing 1 1 24
Profit $40 $60
a. The maximum profit is $1440. The maximum occurs when 0 trick skis and 24 slalom skis are produced
Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $55.
b. The maximum profit decreased to, remained the same at, or increased to $1320
c. The maximum occur when 0 trick skis and 24 slalom skis are produced.
Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $65.
a. The maximum profit decreased to, remained the same at, or increased to $1560. b. maximum occurs when 0 trick skis and 24 slalom skis are produced.
4. The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 63 students, requires 3 chaperones and cost $1,200 to rent. Each van can transport 7 students, requires 1 chaperone, and cost $120 to rent. Since there are 441 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 441 students. Since only 39 parents have volunteered to serve as chaperones, the officers must plan to use at most 39 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
a. The officers should rent 4 buses and 27 vans to minimize the transportation cost.
b. The minimal transportation costs are $8040
5. Indicate if the following is true or false.
{1, 6} ?{1,2,5,6}
__ True
__False
6. Write the resulting set using the listing method.
{3,4,14} ? {4,14,22}={3, 4, 14, 22}
{3,4,14} ? {4,14,22} is a empty set
7. Write the resulting set using the listing method.
{x |x is an eve number between 6 and 14, inclusive}
The resulting set, written in listing notation, is {6, 8, 10, 12, 14}
8. A college offers 3 introductory courses in history, 4 in science, 2 in mathematics, 1 in philosophy and 4 in English.
a. If a freshman takes one course in each during her first semester, how many course selections are possible? 96
b. If a part-time student can afford to take only one introductory course, how any selections are possible? 32
9. You would like to make a salad that consists of lettuce, tomato, cucumber and peppers. You go to the market intending to purchase one variety of each of these ingredients. You discover that there are eight varieties of lettuce, five varieties of tomatoes, two varieties of cucumbers, and four varieties of peppers for sale at the supermarket. How many different salads can you make?
a. You can make 320 different salads type a whole number)
10. A group of 100 people touring Europe includes 52 people who speak Polish, 63 who speak Portuguese, and 14 who speak nether language. How many people in the group speak both polish and Portuguese?
a. 29 people in the group speak both polish and Portuguese.
11. How many ways can a 3-person subcommittee be selected from a committee of 8 people?
How many ways can a president, vice president, and secretary be chosen from a committee of 8 people?
a. The number of ways to select a 3-person subcommittee is 56
b. The number of ways to choose a president, vice president, and secretary is 336
12. Evaluate the expression (simplify your answer)
17!/4!(17-4)!= 2380
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