Answer:
The company should produce 3600 racing bikes, 1800 touring bikes, and 1200 mountain bikes to maximize profit.
Step-by-step explanation:
If you want explanation, I will give you some. (Also please brainliest.)
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Set up the decision variables.
Let x₁ be the number of racing bikes, let x₂ be the number of touring bikes, and let x₃ be the number of mountain bikes.
Define the objective function.
The objective function is the function that we want to maximize. In this case, the objective function is the total profit, which is given by:
z = 7[tex]x_{1}[/tex] + 11[tex]x_{2}[/tex] + 20[tex]x_{3}[/tex]
where: 7, 11, and 20 are the profits for each racing bike, touring bike, and mountain bike, respectively.
Define the constraints.
The constraints are the limitations that we have to consider when making our decisions. In this case, the constraints are:
The total number of steel units used cannot exceed the available amount of steel:
19x₁ + 36x₂ + 38x₃ ≤ 136,800
The total number of aluminum units used cannot exceed the available amount of aluminum:
15x₁ + 24x₂ + 18x₃ ≤ 66,600
The number of bicycles produced must be non-negative:
x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0
The optimal solution will give us the values of x₁, x₂, and x₃ that will maximize the total profit.
