A Farmer Is Planning His Spring Planting Suppose the Farmer Can Purchase More Fertilizer for $2

question 26

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.
$$\begin{array} { l | c c c c c } \text { Crap } & \begin{array} { c } \text { Profitper } \\\text { Acre ( }\end{array} & \begin{array} { c } \text { Yied per } \\\text { Acre (lb) }\end{array} & \begin{array} { c } \text { Meximum } \\\text { Denand (lb) }\end{array} & \begin{array} { c } \text { Irripation } \\\text { (acreft) }\end{array} & \begin{array} { c } \text { Fetilize } \\\text { (pounds/are) }\end{array} \\\hline \text { Carm } & 2,100 & 21,000 & 200,000 & 2 & 500 \\\text { pumplin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300\end{array}$$ Suppose the farmer can purchase more fertilizer for $2.50 per pound, should he purchase it and how much can he buy and still be sure of the value of the additional fertilizer? Base your response on the following Risk Solver Platform (RSP) sensitivity output.
$\text { Changing Cells}$
$\begin{array}{llrrrrr}&&\text { Final } & \text { Reduced } & \text { Objective } & \text { Allowable } & \text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \\\hline \$ B \$ 4 & \text { Acres of Corn } & 9.52 & 0 & 2100 & 1 \mathrm{E}+30 & 350 \\\$ \mathrm{C} \$ 4 & \text { Acres of Pumpkin } & 0 & -500.01 & 899.99 & 500.01 & 1 \mathrm{E}+30 \\\$ \mathrm{D} \$ 4 & \text { Acres of Beans } & 10.79 & 0 & 1050 & 210 & 375.00\end{array}$

$\text { Constraints }$
$\begin{array}{llrrrrr}&&\text { Final } & \text {Shadow } & \text {Constraint } & \text {Allowable } & \text {Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{E} \$ 8 & \text { Corn demand Used } & 200000 & 0.017 & 200000 & 136000 & 152000 \\\$ \mathrm{E} \$ 9 & \text { Pumpkin demand Used } & 0 & 0 & 180000 & 1 \mathrm{E}+30 & 180000 \\\$ \mathrm{E} \$ 10 & \text { Bean demand Used } & 37777.78 & 0 & 80000 & 1 \mathrm{E}+30 & 42222.22 \\\$ \mathrm{E} \$ 11 & \text { Water Used } & 29.84 & 0 & 50 & 1 \mathrm{E}+30 & 20.15 \\\$ \mathrm{~F} \$ 12 & \text { Fertilizer Userl } & 8000 & 35 & 8000 & 3610 ก 4 & 323800\end{array}$

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Definitions:

Time Frames

The periods or durations in which specific tasks or goals should be completed or are expected to take place.

Wrap-Up Stage

The final phase of a process where activities are concluded and summaries or evaluations are provided.

Wrap-Up Stage

The final phase in a process where activities are concluded and matters are brought to a close.

Team Leader

An individual who guides, directs, and motivates a group towards achieving a common goal, demonstrating leadership and organizational skills.