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Question 57116: Identify and graph each of the following.
Identify the inequality which expresses the limitaion for the number of bikes made based on the amount of time available for assembly.
Identify the inequality which expresses the limitation of the number of bikes made based on the amount of time avaliable for painting.
Identify the inequality which expresses the limitation of the number of bikes made based on the amount of time available for packaging.
Identify the objective function that will be used to determine the number of bikes they should produce to maximize the profit each week.
The bike company produces two types of bikes, Model 15A requires 1 hour to assemble, 2 hours to paint and 1 hour to package. Model 17A requires 2 hours to assemble, 3 hours to paint, and 1 hour to package. On a weekly basis the manufacturer has 40 hours available for assemble, 72 hours for painting, and 30 hours available for packaging the bikes. If the profits per bike are $45 for Model 15A and $55 for Model 17A, how many of each model should be made each week to guarantee a maximum profit. What is the profit.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The bike company produces two types of bikes, Model 15A requires 1 hour to assemble, 2 hours to paint and 1 hour to package. Model 17A requires 2 hours to assemble, 3 hours to paint, and 1 hour to package. On a weekly basis the manufacturer has 40 hours available for assemble, 72 hours for painting, and 30 hours available for packaging the bikes. If the profits per bike are $45 for Model 15A and $55 for Model 17A, how many of each model should be made each week to guarantee a maximum profit. What is the profit.
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This is a messy problem.
Let "x" be the number of model15A's produced:
Let "y" be the number of model17A's produced:
x>=0
y>=0
Equation #1: Assembly: x+2y<=40
Equation #2: Paint: 2x+3y<=72
Equation #3: Package: x+y<=30
Profit=45x+55y
You need to find the intersection of #1 with #2; #1 with #3; #2 with #3
You also need find the x and y intercepts of #1, #2, and #3.
All of these poins are potentially the number of x and y items that could
be produced to mind the maximum profit.
I'll let you find these intersecion points and check them in the Profit
equation to find the maximum profit.
Cheers,
Stan H.
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