# Develop complete algebraic and spreadsheet models to illustrate the case of Mr. Soanso.

Applied Management Science

Scenario Requirements

Mr. Soanso and his family own a 100-acre farm where they grow various crops. For the upcoming season, they plan to plant a mix of five crops (Beans, Cucumber, Sweet Corn, Tomatoes, and Watermelon) aiming for a high yield with a 90% assurance level. Mr. Soanso intends to use 2,000 hours of his own labor and another 5,000 hours from family labor, without hiring external help. There are ample seeds and 300 tons of fertilizer available for the season.

The table below shows the labor-hours and tons of fertilizer required per acre, along with the expected profit per ton for each crop:

Crops Beans Cucumber Sweet Corn Tomatoes Watermelon
Labor (Hours/acre) 95 50 85 60 70
Fertilizer (Tons/acre) 4 1.5 3.5 2 3
Expected Profit (\$/ton) 568 649 730 405 486

Mr. Soanso plans to use a low-pressure spray irrigation method and must meet peak water demand as follows:

• Peak water use rate: 0.25 inches per day with 20 daily pumping hours for three days per week.
• Total average daily water consumption on the farm must not exceed 65,000 gallons.

Additionally, Mr. Soanso has the following planting considerations for the season:

• At least 10 acres of cucumbers should be planted.
• The combined planted acres of beans and corn should be at least 20 acres.
• The combined planted acres of beans, cucumber, and tomatoes should be at least 30 acres.
• The planted acres of cucumber and tomatoes should not exceed the 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 and determine the expected quantity of each crop to be produced.

Crops | Beans | Cucumber | Sweet Corn | Tomatoes | Watermelon Water Required (gallons/day) | | | | | Quantity to be produced (tons/acre) | | | | |

Question 2: Develop comprehensive algebraic and spreadsheet models to illustrate Mr. Soanso`s case.

Question 3: Utilize your spreadsheet model to determine the optimal allocation of land (total irrigated area) for each crop to maximize Mr. Soanso`s profit.

Question 4: Provide recommendations to Mr. Soanso based on the results obtained from your analysis.