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A company in the wine production sector is in the production planning process with a horizon of 5 years in each of the cultivation fields

A company in the wine production sector is in the production planning process with a horizon of 5 years in each of the cultivation fields that it recently acquired in the Land A, Land B, Land C and Land D Valleys, which have a usable area of 18 [ha], 10 [ha], 11 [ha] and 16 [ha] respectively. Due to some problems with water management, the company decided that less land area could be used if necessary. This company knows that the first years will not be able to generate income because the plantation takes time to grow, but they do not care since they have the capital and the time necessary to wait. It is for this reason, and based on information that they managed to obtain from other companies in the same field, that they need to plan the production scheme of their vineyards very well

Type of Wine

Work force

Water

Fertilizer

Wine 1

210

2500

8180

Wine 2

250

2700

9000

Wine 3

180

3000

7500

Wine 4

230

2800

8500

Total

13000

600000

150000

The above table applies only to the land located in the LAND B Valley since in LAND C and LAND D it is 85% of the LAND B requirements, while in the LAND A they are 20% more than in LAND B. The conditions of the company indicate that in any of its lands you have the same total availability indicated in the previous table.

Each wine strain has an individual yield, measured in (ton / ha), which is also different in each location, this information is in the following table

Type of Wine

LAND A

LAND B

LAND C

LAND D

Wine 1

29

21

26

25

Wine 2

21

19

19

20

Wine 3

23

21

19

21

Wine 4

26

20

21

22

On the other hand, the earnings for each vine, measured in (Musd $ / ton), also depend on the locality, which is detailed below

Type of Wine

LAND A

LAND B

LAND C

LAND D

Wine 1

6,3

6,2

5,9

5,8

Wine 2

8,0

7,5

7,3

7,4

Wine 3

6,5

6,4

6,1

6,3

Wine 4

6,3

6,1

6,4

6,5

Raise a mathematical model that allows you to maximize your profits (Do not solve just pose). Clearly identify decision variables, objective function, and constraints. Parametrical model.

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