Question 1175633
let x = number of acres of soybeans.
let y = number of acres of wheat.


your constraint inequalities are:


x + y <= 120 (acres of land available)
4x + 5y <= 110 (maintenance days)
65x + 45y <= 2900 (prep dollars)
x >= 0, y >= 0 (number of acres can't be negative)


your objective function is 240x + 155y
this is what you want to maximize.


using the desmos.com calculator, you would graph the opposite of the constraint inequalities.


those are:


x + y <= 120
4x + 5y <= 110
65x + 45y <= 2900
x >= 0, y >= 0


the area on the graph that is not shaded is your region of feasibility.
you would evaluate your objective function at each of the corner points of the feasible region to find your maximum profit.


the graph looks like this:


<img src = "http://theo.x10hosting.com/2021/022203.jpg" >


using the simplex method tool, i got the following results.


<img src = "http://theo.x10hosting.com/2021/022204.jpg" >


both tools lead to the answer being 27.5 acres of soybean planted will yield the maximum profit while still keeping within the constraints.


all the constraint inequalities are satisfied at the maximum profit point.


the point on the graph that has the maximum profit is (x,y) = (27.5,0).


65x + 45y = 1787 <= 2900
x + y = 27.5 <= 120
4x + 5y = 27.5 * 4 = 110 <= 110 *****


maximum profit is 27.5 * 230 = 6325.


it appears the maintenance days constraint is the limiting factor.