Question 1205691
x = the number of regular gadgets.
y = the number of premium gadgets.


you get 3 dollars for every regular gadget and 9 dollars for every premium gadgets.


your constraint inequalities are:
x + y >= 10 
x + 3y <= 60
y >= x
x >= 0
y >= 0


your objective function is:
3x + 9y which you want to maximize.


using the desmod.com calculator at <a href = "https://www.desmos.com/calculator" target = "_blank">https://www.desmos.com/calculator</a>, you would:


graph the opposite of the inequalities.
the area on the graph that is not shaded is your region of feasibility.
you evaluate the objective function at each corner point of that region to find the corner point with the maximum contribution.


it appears that the coordinate points of (0,20) and (15,15) both contain the maximum contribution at 180 dollars each.


you would then decide which one of those you want to do based on other considerations, such as maybe you don't want to just make premium gadgets since there's a market for the regular gadgets as well.


here's what the graph looks like.


<img src = "http://theo.x10hosting.com/2024/011911.jpg">


all the constraint inequalities are asatisfied at each corner point, as they should be.





-