Question

Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2​ labor-hours of assembly and 2​ labor-hours of testing. Each soccer game requires 3​ labor-hours of assembly and 1​ labor-hour of testing. Each day there are 44 ​labor-hours available for assembly and 32 ​labor-hours available for testing. How many of each game should Infotron produce each day to maximize its total daily​ output?

Answer 1

Answer:

Infotron should produce each day 13 hockey and 6 soccer games

Step-by-step explanation:

x = Number of hockey games Infotron should produce

y = Number of soccer games Infotron should produce

Number of labor-hours for assembly = 2x + 3y

Number of labor-hours for testing = 2x + y

Now we can write our equations system, this way:

2x + 3y = 44

2x + y = 32

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Expressing y in terms of x in the 2nd equation:

2x + y = 32

y = 32 - 2x

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Substituting y and solving for x in the 1st equation:

2x + 3y = 44

2x + 3 * ( 32 - 2x) = 44

2x + 96 - 6x = 44

-4x = 44 - 96

-4x = - 52

x = -52/-4

x = 13

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Solving for y in the 2nd equation:

2x + y = 32

2 * 13 + y = 32

26 + y = 32

y = 32 - 26

y = 6

Infotron should produce each day 13 hockey and 6 soccer games