SOLUTION: Hi Audio purchases speakers from a manufacturing company and installs them in its own cabinets. Their model A speaker assembly, which sells for $200 has a tweeter and mid-range spe
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Question 1077460: Hi Audio purchases speakers from a manufacturing company and installs them in its own cabinets. Their model A speaker assembly, which sells for $200 has a tweeter and mid-range speaker. The model B Assembly, which sells for $350, has two tweeters, mid-range and a woofer. Hi Audio currently has in stock 90tweeters, 60 mid-range speakers, and 44 woofers. How many speaker assemblies of each should they make to maximize revenue? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let r = revenue
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
