A Farmer Is Planning His Spring Planting Enter the Numbers in the Appropriate Cells of Ranges B12:D12

question 1

Essay

A farmer is planning his spring planting.He has 20 acres on which he can plant a combination of Corn,Pumpkins and Beans.He wants to maximize his profit but there is a limited demand for each crop.Each crop also requires fertilizer and irrigation water which are in short supply.There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available.The following table summarizes the data for the problem.
$\begin{array}{l|clccc}&\text { Profit per } & \text { Yield per } & \text { Maximum } & \text { Irrigation } & \text { Fertilizer } \\\text { Crop }&\text { Acre } \$) & \text { Acre } 1 \mathrm{~b} \text { ) } & \text { Demand } \mathrm{lb} \text { ) } & \text { acre } \mathrm{ft}) & \text { pounds/acre) }\\\hline\text { Corn } & 2,100 & 21,000 & 200,000 & 2 & 500 \\\text { Pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300\end{array}$
Enter the numbers in the appropriate cells of ranges B12:D12 and E8:F12 in the Excel spreadsheet to solve this problem based on the following formulation.
Let ^X₁ ^{= aces of corn}
X₂ = acres of pumpkin X₃ = acres of beans
MAX: ^2100X₁ ^{+ 900X}₂ ^{+ 1050X}₃
Subject to: ^21X₁ ^{≤ 200}
10X₂ ≤ 180
3.5X₃ ≤ 80
X₁ + X₂ + X₃ ≤ 20 2X₁ + 3X₂ + 1X₃ ≤ 50
5X₁ + 4X₂ + 3X₃ ≤ 80 X₁,X₂,X₃ ≥ 0
$\begin{array}{|c|c|c|c|c|c|c|} \hline& \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & & \text { Farm } & \text { Planning } & \text { Problem } & & \\\hline 2 & & & & & & \\\hline 3 & & \text { Corn } & \text { Pumplin } & \text { Beans } & & \\\hline 4 & \text { Acres to plant } & & & & & \text { Total Profit: } \\\hline 5 & \text { Profit per acre } & & & & & \\\hline 6 & & & & & & \\\hline 7 & \text { Constraints: } & & & & \text { Used } & \text { Available } \\\hline 8 & \text { Corn demand } & & & & & \\\hline 9 & \text { Pumpkin demand } \\\hline 10 & \text { Bean demand } \\\hline 11 & \text { Water } \\\hline 12 & \text { Fertilizer } \\\hline\end{array}$

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Definitions:

Order Cycle Times

The duration between when a customer places an order and when they receive the product, often a critical metric in supply chain management.

Administrative Costs

Expenses related to the general operation of a business, including salaries of office staff, rent, and utilities.

Unambiguous Description

A clear, precise, and specific explanation or depiction that avoids confusion or misinterpretation.

Best Value

Refers to the most advantageous combination of cost, quality, and sustainability to achieve the greatest net benefit.