SOLUTION: A telephone company manufactures two diffrent models of phones: Model 120 is cordless and model 140 is not cordlss it takes 1 hour to manufacture the cordless phone and 1 hour and

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Question 1067708: A telephone company manufactures two diffrent models of phones: Model 120 is cordless and model 140 is not cordlss it takes 1 hour to manufacture the cordless phone and 1 hour and 30 mimuntes to manufacture the tradtional phone. at least 300 of the cordless models are to be produced the manufavturer realizes a profit per phone of $12 afor model 120 and $10 for model 140, If at most 1000 hours are to be allocated to the manufacture of both phones combined how many of each model should be produced to maximize total profit.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your objective function is p = 12x + 10y

p is the profit.
x is the number of cordless phones.
y is the number of landline phones.

your constraint equations are:

x >= 300
x + 3/2 * y <=1000
y >= 0

x >= 300 because the number 0of cordless phone has to be greater than or equal to 300.
y >= 0 because the number of landline phones has to be greater than or equal to 0.
x + 3/2 * y <= 100 because the total manufacturing hours have to be less than 1000 and it takes 1 hour to manufacture a cordless phone and 3/2 hours to manufacture a landline phone.

using the desmos calculator (www.desmos.com/calculator), you would graph the opposite inequalities and the unshaded region is your feaqsible region.

the corner points of your feasible region are the max/min values for your objective function.

your constraint equations are, once again:

x >= 300
x + 3/2 * y <=1000
y >= 0

you would graph:

x <= 300
x + 3/2 * y >=1000
y <= 0

your graph will look like this:

$$$

the corner points of your graph are at:

(300,466.667)
(300,0)
(1000,0)

your objective function of p = 12x + 10y yields the following profite at each of these corner points respectively.

8266.67
3600
12000

to maximize your profit, you need to manufacture 1000 cordless phones and 0 landline phones.

your constraints need to be met.
total hours to manufacture is less than or equal to 1000 (met).
number of cordles phones greater than or equal to 300 (met).
number of landline phones greater than or equal to 0 (met).

solution looks good.