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avanturin [10]
3 years ago
8

Find the solutions of the form x=a,y=0and x=0 ,y=b for the following equations: 2x+5y=10 and 2x+3y=6. is there any common soluti

on?
Mathematics
1 answer:
Arlecino [84]3 years ago
8 0

Answer:

 x=0 and y=2

Step-by-step explanation:

We have been given system of equations:

2x+5y=10     (1)

And 2x+3y=6     (2)

Subtract equation (2) from(1) we get:

2y=4

y=2

Now, substitute y=2 in equation(2) we get:

2x+3(2)=6

2x+6=6

2x=0

x=0

Hence, x=0 and y=2


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tester [92]

The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

16 chairs; 24 tables

Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552

Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608  

15 chairs; 18 tables

Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450

Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480  

12 chairs; 28 tables

Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564

Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636  

18 chairs; 20 tables

Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516

Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544

Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

15 x 65 + 18 x 90 = X

975 + 1,620 = X

2,595 = X

Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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We have the following:

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