Finite Mathematics Applied to the Real World
Arranged by Topic
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| Review Exercise Index | | Quiz Index | | Summary Index | | Return to Main Page |
| | Functions and Graphs |
| | Systems of Linear Equations |
| | Sets and Counting |
| | Markov Processes |
Question 1
Find the maximum value of p = 6x + y subject to:
15
10
2x
0, y 0
| Answer |
O'Hagan Bookworm Booksellers buys books from two publishers. Duffin House offers a package of 5 mysteries and 5 romance novels for $50, and Gorman Press offers a package of 5 mysteries and 10 romance novels for $150. O'Hagan wants to buy at least 2,500 mysteries and 3,500 romance novels, and he has promised Gorman (who has influence on the Senate Textbook Committee) that at least 25% of the total number of packages he purchases will come from Gorman Press. How many packages should O'Hagan order from each publisher in order to minimize his cost and satisfy Gorman? What will the novels cost him?
| Answer |
Maximize p = x + 2y + 3z subject to:
+ z 6
20
3y + 4z 30
0, y 0, z 0
| Answer |
Minimize C = x + 2y + 3z subject to
500,
700,
y + 3z 0
0, y 0, z 0
| Answer |
Senator Porkbarrel overdraws his accounts at the following banks: the Congressional Integrity Bank, Citizens' Trust, and "Checks R Us." There are no penalties for these withdrawals since the overdrafts are subsidized by the taxpayer. The Senate Ethics Committee tends to let slide irregular banking activities of this sort, provided they are not flagrant. At the moment (due to Congress' preoccupation with a Supreme Court nominee) a total overdraft of up to $10,000 will be overlooked. Porkbarrel's underlying sense of guilt makes him feel funny about writing overdrafts for banks whose names include expressions like "integrity" and "citizens' trust." The effect of this is that his bad check writing for the first two banks combined amounts to no more than one-quarter of the total. On the other hand, the financial officers at Integrity Bank are eager to please Senator Porkbarrel due to his influential position on the Senate Banking Committee, so they would like him to overdraw his account by as much as possible. Find the amount he should draw from each bank in order to avoid investigation by the Ethics Committee and overdraw his account at Integrity by as much as his sense of guilt will allow.
| Answer |
Your software company has launched the latest version of its web browser, "Java Cruise 4.0." As sales manager, you are planning to promote Java Cruise 4.0 by sending sales forces to software conventions running concurrently in Saint Louis and Detroit. You have 6 representatives available at each of your Little Rock, Ark. and Urbana, Ill. branches, and you would like to send at least 5 to the Saint Louis convention and at least 4 to the Detroit convention. The Saint Louis convention will last for three days, while the Detroit convention will last for two days. Air fares (per person) and hotel accommodation costs (per person) are shown in the following figure.
How many representatives should you send from each branch to each convention in order to minimize the total (air travel and accommodation) cost? What will the total cost amount to?
| Answer |
Minimize C = 50x + 150y + 100z subject to
2,500,
3,500,
y + 3z 0
0, y 0, z 0
| Answer |
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| Stefan Waner (matszw@hofstra.edu) | | Steven R. Costenoble (matsrc@hofstra.edu) |