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

question 68

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.
$$\begin{array} { l | c c c c c } \text { Crop } & \begin{array} { c } \text { Profit per } \\\text { Acre } ( \$ )\end{array} & \begin{array} { c } \text { Yield per } \\\text { Acre (Ib) }\end{array} & \begin{array} { c } \text { Maximum } \\\text { Demand (Ib) }\end{array} & \begin{array} { c } \text { Irrigation } \\\text { (acre ft) }\end{array} & \begin{array} { c } \text { Fertilizer } \\\text { (pounds/acre) }\end{array} \\\hline \text { Corn } & 2,100 & 21,000 & 200,000 & 2 & 500 \\\text { Pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300\end{array}$$ 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
$\begin{array} { l } X _ { 1 } = \text { aces of corn } \\X _ { 2 } = \text { acres of pumpkin } \\X _ { 3 } = \text { acres of beans }\end{array}$

MAX: $\quad 2100 \mathrm { X } _ { 1 } + 900 \mathrm { X } _ { 2 } + 1050 \mathrm { X } _ { 3 }$
Subject to: $\quad 21 X _ { 1 } \leq 200$
$10 \mathrm { X } _ { 2 } \leq 180$
$3.5 \mathrm { X } _ { 3 } \leq 80$
$\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } \leq 20$
$2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } + 1 \mathrm { X } _ { 3 } \leq 50$
$5 \mathrm { X } _ { 1 } + 4 \mathrm { X } _ { 2 } + 3 \mathrm { X } _ { 3 } \leq 80$
$\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } \geq 0$ $$\begin{array} { | c | l | c | c | c | c | c | } \hline & { \text { A } } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & & \text { Farm } & \text { Planning } & \text { Problem } & & \\\hline 2 & & & & & & \\\hline 3 & & \text { Corn } & \text { Pumpkin } & \text { Beans } & & \\\hline 4 & \text { Acres to plant } & & & & & \text { Total Profit: } \\\hline 5 & \text { Profit per acre } & & & & & \\\hline 6 & & & & & & \\\hline 7 & \text { Constraints: } & & & & \text { Used } & \text { Available } \\\hline 8 & \text { Corn demand } & & & & & \\\hline 9 & \text { Pumpkin demand } & & & & & \\\hline 10 & \text { Bean demand } & & & & & \\\hline 11 & \text { Water } & & & & & \\\hline 12 & \text { Fertilizer } & & & & & \\\hline\end{array}$$

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Definitions:

Consolidated Common Stock

Represents the aggregation of common stock of a parent company and its subsidiaries, shown in the consolidated financial statements.

Acquisition Transaction

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Common Stock

A type of equity security that represents ownership in a corporation, entitling the holder to a share of the company's profits through dividends and/or capital appreciation.

Par Value

A nominal value assigned to share certificates of a company, which has no impact on market value but may affect legal capital.