let x = number of model A speaker assemblies.
let y = number of model B speaker assemblies.
model A speaker has 1 tweeter and 1 mid-range speaker assembly.
model B speaker has 2 tweeters and 1 mid-range and 1 woofer speaker assembly.
number of tweeter speaker assemblies in stock is equal to 90.
number of mid-range speaker assemblies in stock is equal to 60.
number of woofer speaker assemblies in stock is equal to 44.
your revenue function is r = 200x + 350y
this is the function that you want to maximize.
your constraint functions are:
x + 2y <= 90 (each model A needs 1 tweeter and each model B needs 2)
x + y <= 60 (each model A and each model B need 1 mid-range each)
y <= 44 (each model B needs 1 woofer and each model A doesn't need any)
x >= 0
y >= 0
you graph the constraint functions to find the area of feasibility and then you look for the corner points of the feasible region to find the least cost solution.
using the desmos.com, you would graph the opposite of the inequalities and then look for the area on the graph that is not shaded.
you would graph the following inequalities:
x + 2y >= 90
x + y >= 60
y >= 44
x <= 0
y <= 0
your graph would look like this:
your maximum revenue is when x = 30 and y = 30
all the constraints are satisfied.
that's your solution.
when x = 30 and y = 30:
revenue = 30 * 200 + 30 * 350 = 16,500
number of tweeters = 30 * 1 + 30 * 2 = 90 which is <= 90.
number of mid-range speaker assemblies = 30 * 1 + 30 * 1 = 60 which is <= 60.
number of woofers = 30 * 1 = 30 which is <= 44.
you may check for yourself to determine that the max revenue is when x = 30 and y = 30.
the other options are:
x = 0 and y = 44
x = 2 and y = 44
x = 60 and y = 0
x = 0 and y = 0
desmos.com calculator can be found at https://www.desmos.com/calculator