A farmer has 90 acres available for planting millet and alfalfa. Seeds cost $4 per acre for millet and $6 per acre for alfalfa. Labor costs are $20 per acre for millet and $10 per acre for alfalfa. The expected income is $110 per acre for millet and $150 per acre of alfalfa. The farmer intends to spend no more than $480 for seed and $1400 for labor. Find the income for the given constraints. Using Linear Programming to Solve Real Life Problems

By: Maddie Uilk Constraints:

4x + 6y ≤ 480

20x + 10y ≤ 1400

x + y ≤ 90

x ≥0

y ≥ 0 Define Variables:

x = millet

y = alfalfa Step 2: Step 1: Step 3: Find the feasible region: Simplified Constraints:

y ≤ -2/3x + 80

y ≤ -2x + 140

y ≤ -x + 90

x ≥ 0

y ≥ 0 Step 4: A= (0,0)

B= (0, 80)

C= (30,60)

D= (50,40)

E= (20,0) A B C D E Step 5: Profit Statement:

P= 110x + 150y P= 110x + 150y

A (0,0) =$0

B (0,80) =$12,000

C (30, 60) = $12,300

D (50,40) = $11,500

E (20,0) = $7,700 1)

2)

3)

4)

5) 1)

2)

3)

4)

5) Step 6: Profit Statement:

In order to maximize income of $12,300 the farmer needs to sell 30 millet acres and 60 alfalfa acres. Find Vertices: Need to Find C:

4x + 6y ≤ 480

x+ y ≤ 90 4x + 6y ≤ 480

4(x + y ≤ 90) 4x + 6y ≤ 480

4x + 4y ≤ 360

____________

2y ≤ 120

____________

2

Y≤ 60 - 4x + 6(60) ≤ 480 4x + 360 ≤ 480 - 360 360 _______________ 4x ≤ 120

_______

4

X≤ 30 Need to Find D:

20x + 10y ≤ 1400

x + y ≤ 90 20x + 10y ≤ 1400

10(x + y ≤ 90) 20x + 10y ≤ 1400

10x + 10y ≤ 900

_______________

10x ≤ 500

__________

10

X≤ 50 - x(50) + y ≤ 90

50 + y ≤ 90

50 50

____________

Y≤ 40 - A: P=110(0) + 150(0) = 0

B: P=110(0) + 150(80) = 12,000

C: P=110(30) + 150(60) = 12,300

D: P=110(50) + 150(40)= 11,500

E: P=110(20) + 150(0) = 7,750 4x + 6y ≤ 480

-4x -4x

______________

6y ≤ -4x + 480

______________

6

Y ≤ -2/3x + 80 20x + 10y ≤ 1400

-20x 20x

________________

10y ≤ -20x + 1400

_________________

10

Y≤ -2x + 140 x + y ≤ 90

-x -x

___________

Y ≤ -x + 90

### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start remote presentation- Invited audience members
**will follow you**as you navigate and present - People invited to a presentation
**do not need a Prezi account** - This link expires
**10 minutes**after you close the presentation - A maximum of
**30 users**can follow your presentation - Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

### Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.

You can change this under Settings & Account at any time.

# Linear Programming Problem Solving

No description

by

Tweet