Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Expert Solution & Answer
Chapter 4, Problem 16RP
a.
Explanation of Solution
- Consider the following variables:
- x1 = items of type 1
- x2 = items of type 2
- Weight of item is a1 lb and item 2 weighs a2 lb.
- Therefore, the constraints is a1x1+a2x2 ≤ b
- Each type 1 item carries a benefit of c1 units, each type 2 item carries a benefit of c2 units...
- x1 = items of type 1
- x2 = items of type 2
b.
Explanation of Solution
- from the result of part (a), it can be observed that the constraint in linear
programming problem is less than or equal to type.
- So, add the slack variable s1 to the constraint.
- Thus, the standard form of the linear programming problem is,
- Max z= c1x1+c2x2
- Subject to constraints,
- a1x1+a2x2+s1 = b
- The initial simplex table is shown below:
z x1 x2 s1 rhs Basic variable 1 -c1 -c2 0 0 z = 0 0 a1 a2 1 b s1 = b
- Now, there are two negative entries in the row0, suppose the most negative entry is in column 2.
- Therefore, choose entering variable to be x2.
- The leaving variable is calculated with the use of the following formula,
- Leaving variable = {(rhs/x1), x1 ≥ 0}
- Consider the below table:
z x1 x2 s1 rhs Basic variable 1 -c1 -c2 0 0 - 0 a1 a2 1 b (b/a2)→
- From the above table, the pivot table is intersection of both entering and leaving variables...
- Max z= c1x1+c2x2
- Subject to constraints,
- a1x1+a2x2+s1 = b
| z | x1 | x2 | s1 | rhs | Basic variable |
| 1 | -c1 | -c2 | 0 | 0 | z = 0 |
| 0 | a1 | a2 | 1 | b | s1 = b |
- Leaving variable = {(rhs/x1), x1 ≥ 0}
| z | x1 | x2 | s1 | rhs | Basic variable |
| 1 | -c1 | -c2 | 0 | 0 | - |
| 0 | a1 | a2 | 1 | b | (b/a2)→ |
c.
Explanation of Solution
- The following are the assumptions that are violated by this formula:
- Deterministic Nature
- Additivity
- Direct Proportionality
- Fractionally
- The follo...
- Deterministic Nature
- Additivity
- Direct Proportionality
- Fractionally
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Assuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he / she completes university. If he / she does not complete university. If he / she does not complete university, the payment is stopped at the time theta / she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, the person who are less than 18 years or 30 years and above do not qualify to enroll in the program.
a. Request a persons name, age, what he / she wants to do (go to school or learn a trade), time of exit if any and disqualify the person if he / she does not meet the age criteria
b. Compute the total investment made for the person if he / she either finishes or
exited along the way
c. Display the results
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Assuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he/she completes university. If he/she does not complete university, the payment is stopped at the time he/she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, and invest GHC 70 a month till age 30 years. If the person does not complete the apprenticeship, the payment is stopped at the time he/she exited. Remember that persons who are less than 18 years or 30 years and above do NOT qualify to enroll on this program. You are to write a c++ program for the above scenario. Your program should a) compute the total investment made for the person if he/she either finishes or exited along the way. b) display the results.
Chapter 4 Solutions
Introduction to mathematical programming
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7P
Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
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