Question 1172680
the graphical solution is shown below.


<img src = "http://theo.x10hosting.com/2021/010801.jpg" >


the simplex method tool solution is shown below:


<img src = "http://theo.x10hosting.com/2021/010802.jpg" >


both tell you that the optimum solution is when x = 7.143 and y = 57.143.
the graphical solution is rounded to 3 decimal places.
the simplex method tool solution rounds to 6 significant digits.
rounding to decimal digits only includes the fractional part of the answer.
rounding to significant digits includes the whole and fractional part of the answer.


the minimal cost is 2178580 from the graphical solution and 2178570 from the simplex method tool solution.


with the graphical solution, using the desmos.com calculator, you graph the opposite of the constraint inequalities.
the region of feasibility is the area on the graph that is not shaded.
the corner points of the region of feasibility are where the optimum solutions lie.
you evaluate the objective function at each of these corner points to find the minimal cost solution.


the graphical solution shows all the possible values of x and y, one of which will provide the optimal solution.
the simplex method tool only shows optimal solution.


all the constraints need to be satisfied at the optimal solution.
with (7.143, 57.143):
40x + 30y = 2000.01 which is >= 2000.
30x + 40y = 2500.01 which is >= 2000.
20x + 50y = 3000.01 which is >= 3000.
keep in mind that these are rounded numbers, so the answers won't necessarily be right on.


with the simplex method tool, you can set the rounding.
for example, it was set at 6 significant digits.
this will get you closer to the actual results.
it can also be set to greater than 6 significant digits.
i set it to 12 significant digits and this is what is said:
Optimal Solution: c = 2178571.42857; x = 7.14285714286, y = 57.1428571429


the desmos.com calculator can be found at <a href = "https://www.desmos.com/calculator" target = "_blank">https://www.desmos.com/calculator</a>


the simplex method tool can be found at <a href = "https://www.zweigmedia.com/RealWorld/simplex.html" target = "_blank">https://www.zweigmedia.com/RealWorld/simplex.html</a>


your objective function was:
cost = 25000x + 35000y
this you want to minimize.


your constraint inequalities were:
40x + 30y >= 2000 (hi)
30x + 40y >= 2000 (med)
20x + 50y >= 3000 (lo)
x >= 0
y >= 0


i'll be available to answer any questions you might have regardng this.
theo