A Farmer Is Planning His Spring Planting What Are the Key Formulas for This Excel Spreadsheet Implementation

question 51

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. The following table summarizes the data for the problem.
$\begin{array} { l | c c c c c } & \text { Profit per } & \text { Yield per } & \text { Maximum } & \text { Irrigation } &\text { Fertilizer }\\\text { Crop } &\text { Acre(\$)}&\text { Acre (lb) } & \text { Demand (lb) } & \text { (acre ft) }&\text { (pounds/acre) }\\ \hline \text { Corn } & 2,100 & 21,000 & 20,000 & 2 & 500 \\\text { pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & \text { Ba,000 } & 1 & 300\end{array}$
What are the key formulas for this Excel spreadsheet implementation of the following formulation?
$\begin{array} { ll } \text { Let }&\mathbf { X } _ { 1 } = \text { aces of carm } \\&X _ { \mathbf { z } } = \operatorname { acres } \text { of punglan } \\&\mathbf { X } _ { \mathbf { 3 } } = \text { acres of beans } \\\text { MAX: }& \ 2100 X _ { 1 } + 900 X _ { 2 } + 1050 X _ { 3 } \\\text { Subject to: } &21 X _ { 1 } \leq 200 \\&10 \mathrm { X } _ { 2 } \leq 180 \\&3.5 \mathrm { X } _ { 3 } \leq 80 \\&2 X _ { 1 } + 3 X _ { \mathbf { 2 } } + 1 X _ { 3 } \leq 50 \\&5 X _ { 1 } + 4 X _ { 2 } + 3 X _ { 3 } \leq 80 \\&X _ { 1 } , X _ { 2 } X _ { 3 } \geq 0 \\\end{array}$ $$\begin{array} { | c | c | c | c | c | c | c } \hline & { \mathrm { A } } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } \\\hline 1 & & \text { Farm } & \text { Plenning } & \text { Prablem } & & \\\hline 2 & & & & & & \\\hline 3 & & \text { Carn } & \text { Pumpkin } & \text { Benns } & & \\\hline 4 & \text { Acres ta plant } & & & & & \text { Tatal Prafit: } \\\hline 5 & \text { Prafit per acre } & 2100 & 900 & 1050 & & \\\hline 6 & & & & & & \\\hline 7 & \text { Constraints: } & & & & \text { Used } & \text { Available } \\\hline 8 & \text { Corn denand } & 21000 & & & & \text { 200000 } \\\hline 9 & \text { Pumpkin demand } & & 10000 & & & 180000 \\\hline 10 & \text { Bean demand } & & & 3500 & & \text { 80000 } \\\hline 11 & \text { Water } & 2 & 3 & 1 & & 50 \\\hline 12 & \text { Fetilizer } & 500 & 400 & 300 & & 8000 \\\hline\end{array}$$

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Definitions:

Nitrogenous Compounds

Organic or inorganic compounds containing nitrogen in various chemical forms, important in many biological processes and industrial applications.

Organic Nitrogen

Nitrogen that is found in organic compounds, including proteins, nucleic acids, and other naturally occurring organic molecules.

Empowerment

Authorization and enablement; the awakening, liberation, and inspiration of people. Principles of empowerment include trust in people, investment in people, recognition of accomplishment, and decentralized decision making. Empowerment is closely associated with the concepts of democratic and participative leadership.

Metaphor

A figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable, often for comparison or symbolic purposes.