Applied Management Science
Mr. Soanso and his family have a 100-acre farm which they use for growing various crops. The family is planning to plant a mix of five crops (Beans, Cucumber, Sweet Corn, Tomatoes, and Watermelon) for the upcoming season, aiming for a high yield goal with 90% assurance level. Mr. Soanso is not planning to hire any external labor during the upcoming season - he will be making use of 2,000 hours of his own and another 5,000 hours of labor available from his family. There are sufficient amount of seeds and 300 tons of fertilizer available to utilize during the upcoming season.
The table below provides details about the labor-hours and tons of fertilizer required per acre, as well as the total expected
|Required Labor (Hours/acre)||95||50||85||60||70|
|Required Fertilizers (Tons/acre)||4||1.5||3.5||2||3|
|Expected Profit ($/ton)||568||649||730||405||486|
Mr. Soanso wishes to use a low-pressure spray method for irrigating the crops and would need to meet peak irrigation water demand as per the following:
- The peak water use rate is 0.25 inches per day with 20 daily pumping hours for three days per week.
- The total average daily consumption of water in the farm does not exceed 65,000 gallons.
In addition, Mr. Soanso has the following demand considerations for the upcoming season:
- At least 10 acres of cucumbers should be planted
- The total planted acres of beans and corn should be at least 20 acres
- The total planted acres of beans, cucumber, and tomatoes should be at least 30 acres
- The total planted acres of cucumber and tomatoes should not exceed the total planted acres of beans, sweet corn, and watermelon
Question 1: Refer to the Irrigation Fact Sheet to estimate the average daily water requirement for each crop using the pro page 4. Also determine the expected quantity of the five crops to be produced.
|Average daily water required (gallons/day)|
|Quantity to be produced (tons/acre)|
Question 2: Develop complete algebraic and spreadsheet models to illustrate the case of Mr. Soanso.
Question 3: Use your spreadsheet model to determine how much land (total area irrigated) should be devoted to each of maximize Mr. Soanso`s profit.
Question 4: Provide recommendations to Mr. Soanso based on the obtained results using your own words.