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This is a Linear Programming

Resolved Question:

This is a Linear Programming problem that provides a solution that provides the following:
- Objective Function
- Decision Variables
- Constraints

PROBLEM:
The Hogg company are a group of Oklahoma agricultural producers. The Hoggs want to derive a production process that will satisfy their goals. These farmers can produce corn, wheat, and/or hogs. The acreage they can cultivate for crops is 1100 acres, of which 600 acres is for corn production and 500 acres for wheat production. The Hogs have a maximum of 2000 hr of labor available for crop operations and 600 hr of labor for their hog operation. Corn production requires 1.6 hr of labor per acre, wheat requires 2.0 hr of labor per acre, and the hog operation requires 20 hr of labor per hog unit. This farm can produce 120 bushel of corn per acre and 32 bushel of wheat per acre. Corn and wheat can be sold on the market at $2.50 per bushel and $2.35 per bushel, respectively, and/or can be used as feed in the hog operation. Also, corn and wheat may be purchased from the city feed store at $2.70 per bushel and $2.55 pr bushel, respectively, for feeding the hogs. The hog unit requires 169.1 bushel of feed during a single production period. The corn and wheat used as hog feed can be transformed into corn equivalent units; that is, 1.1 bushel of wheat equals 1 bushel of corn.

The cost per acre to produce corn and wheat are $146.40 per acre and $48.60 per acre. The returns to the hog operation are $919.20 per hog unit. A hog unit is a sow and her litter, which are sold on the market. Returns to the hog operation are net values, for example, after maintenance and replacement stock cost.

The Hogg company is considering the following strategy:

Strategy 1 (There are no other strategies being considered)
As the goal with the highest priority, P1 they would like to see returns to the agriculture operation of at least $100,000. As their second priority, P2, at least three fourths of the land available for corn production and at least one-half of the land available for wheat production must be planted. The producers also desire that the under-planting of corn be weighed three times greater than that for wheat. The third and last priority goal P3, is that the hog operation be no greater than 40 hog units.

Formulate the problem in a goal programming format and solve for strategies 1 and 2. Discuss the results of whether the goals were achieved in each strategy and the corn, wheat and hog production output.
Submitted: 2 years ago.
Category: Homework
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Ray Atkinson, Graduate Student
Category: Homework
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Experience: Degrees in Math, Education and Accounting, years and years of tutoring.
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Customer: replied 2 years ago.

Ok. Thanks. The hog units ($919.2) and (max 40 labor hurs) was really throwing me for a loop.

 

So the Objective Function and Constraints should read as follows, correct?

 

MAX 153.6C + 26.6W

 

S.T. C + W <= 2000

1.6C + 2W <= 2000

 

Yes, if you will favor me with some additional explanation. What about the hog hrs? Where do the hog hrs fit into the above formula since it was restricted to <= 40hrs? I'm not sure I understand how it is being left out of the formula, yet able to be addressed in the solution. This is where my downfall in solving this problem has occurred.

 

Thanks

 

ps.: I have one more problem that I've started, but have not finished yet. Are you interested in assisting me with that one as well? If yes, I will get it posted. Let me know. Thanks.

 

 

Expert:  Ray Atkinson replied 2 years ago.
I think the person making the problem was using an old problem and changed the numbers without thinking it through. Observe the 600 hours of hog labor available and 20 hours of labor each. This restricts the number of hog units to 30, so there is no way to even get to the 40 restriction.
The solution I gave is not the most money that the company can get, but it does satisfy all the given conditions for success.

You can post the next problem. Put my name on it and I will be the one to answer.
Customer: replied 2 years ago.

Ah. Ok. I did not make that connection. Thanks for clarifying.

 

I'm going to post my next question now.

Expert:  Ray Atkinson replied 2 years ago.
I cannot answer that one. I do not know how to do it.

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