QUESTION $2(40$ marks$)$

A farmer in Iowa owns $45$ acres of land. He is going to plant each acre with wheat and corn. Each acre planted with wheat yields $$200$ profit, requires $3$ workers, and requires $2$ tons of fertilizer; each acre planted with corn yields $$300$ profit, requires $2$ workers, and requires $4$ tons of fertilizer. $100$ workers and $120$ tons of fertilizer are available.

What are the two decisions that need to be made by the farmer? $(4$ marks$)$

Set up the above problem in Excel using the style that we used in class. Make sure that your spreadsheet model is logical$,$ well organized and easy to understand. In building formulas, use the sumproduct function where appropriate. Use text boxes to identify the changing cells, target cell and constraints. $(15$ marks$)$

Solve the problem using Solver. Assuming the farmer wants to maximize the profit from the land, what would be your recommendation to the farmer in terms of planting the crops? $(3$ marks$)$

How much of the land will not be planted in crops? $(1$ mark$)$

Which constraints are binding? non$-$binding? $(2$ marks$)$

Print out your spreadsheet model in landscape orientation and include it you$$re your answers. You do NOT need to use a color printer. $(5$ marks$)$

Print out the cell formulas in landscape orientation and include it with your answers. $(5$ marks$)$

For this question only, assume that the farmer now has $107$ workers available. What would be your recommendation now? Do these decimal numbers make sense? Explain. $(5$ marks$)$