Question 1175634
x = number of items of A.
y = number of items of B.


labor = 3x + 4y <= 3000 minutes per day.
raw materials = 2x + y <= 1000 dollars per day.


profit is equal to 5x + 4y dollars.
this is your objective function.
it's what you want to maximize.


you can solve this graphically using the desmos.com calculator.


using that calculator, you graph the opposite of the inequalities.
the feasible region is the area of the graph that is not shaded.


your constraint inequalities are:


3x + 4y <= 3000
2x + y <= 1000
x >= 0
y >= 0


you are graphing the opposite of these inequalities.
you are evaluating the objective functio0n at the corner points of the feasible region.
the feasible region is the area on the graph that is not shaded.


evaluation of the corner points yields the maximum profit at (200,600).
the maximum profit is 3400 dollars.
all the constraint inequalities are satisfied at this point.


the graph looks like this.


<img src = "http://theo.x10hosting.com/2021/022202.jpg" >


i also used a simplex method tool that provide the same answer.


the results of using that tool are shown below.


<img src = "http://theo.x10hosting.com/2021/022201.jpg" >


the 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