Weekly Homework Group 4
Week – 9
Professor Ryan Brownlee
Group Members
1. Pitiyavarun Sivanesasuntharam (101540762)
2. Magdiel Rebelo (101533146)
3. Needesh Selvakumar (101494357)
4.Avinash Suryawanshi- 101436278
9_14
A farmer in the Midwest has 1,000 acres of land on which she intends to
plant corn, wheat, and soybeans. Each acre of corn costs $100 for
preparation, requires 7 worker-days of labor, and yields. a profit of $30. An
acre of wheat costs $120 to prepare, requires 10 worker-days of labor, and
yields $40 profit. An acre of soybeans costs $70 to prepare, requires 8
worker-days, and yields $20 profit. The farmer has taken out a loan of
$80,000 for crop preparation and has contracted with a union for 6,000
worker-days of labor. A midwestern granary has agreed to purchase 200
acres of corn, 500 acres of wheat, and 300 acres of soybeans. The farmer
has established the following goals, in order of their importance:
(1) To maintain good relations with the union, the labor contract must be
honored; that is, the full 6,000 worker-days of labor contracted for must be
used.
(2) Preparation costs should not exceed the loan amount so that additional
loans will not have to be secured.
(3) The farmer desires a profit of at least $105,000 to remain in good
financial condition.
(4) Contracting for excess labor should be avoided.
(5) The farmer would like to use as much of the available acreage as
possible.
(6) The farmer would like to meet the sales agreement with the granary.
However, the goal should be weighted according to the profit returned by
each crop.
a. Formulate a goal programming model to determine the number of acres of
each crop the farmer should plant to satisfy the goals in the best possible
way.
b. Solve this model by using the computer.
Let
X1 be the number of acres of corn to plant.
X2 be the number of acres of wheat to plant.
X3 be the number of acres of soyabeans to plant.
1. Profit Maximization: Maximize the total profit.
[Maximize 30x1 + 40x2 + 20x3]
2. Goal Prioritization:
- Maintain Labor Contract: Use exactly 6,000 worker-days of labor.
[Subject to 7x1 + 10x2 + 8x3 = 6,000]
- Cost Constraint: Keep total preparation costs within the loan amount.
[Subject to 100x1 + 120x2 + 70x3 < 80,000]
- Desired Profit: Achieve a profit of at least $105,000.
[Subject to 30x1 + 40x2 + 20x3 ≥ 105,000]
Sales Agreement:
Granary's Purchase Agreement:
[Subject to x1 = 200, x2 = 500,
x3=300］
9_52
To determine the best city for the Blitz professional soccer team to relocate,
we will use the scoring model with the provided weighted criteria and grades
for each city. We will calculate the weighted scores for each city and
determine the city with the highest total score.
The formula to calculate the score for each city is:
Total Score=∑(Weight×Grade)
Let's calculate the total score for each city (Atlanta, Birmingham, Charlotte,
and Durham).
The city with the highest total score is the recommended relocation city,
which is Durham, with 74.25.
