Question

The Cruiser Bicycle Company makes two styles of bicycles: the Traveler, which sells for $200, and the Tourister, which sells for $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor available for production. How many bicycles of each model should be produced to maximize revenue?

Answer 1

tiffany

Answer 2

yes?

Answer 3

1) Let the number of Traveler be 'x' and that of Tourer be 'y'.

2) As per the given constraints, x + y </= 300 --------- (1) and x + 3y </= 360 ----- (2)

3) Also, x >/= 0 and y >/= 0, since negative production of each are not possible.

4) The objective of the modeling is to maximize revenue which is given by R = 200x + 600y

You may now plot a graph of four lines, given by x + y = 300, x + 3y = 360, x = 0 and y = 0.

We will get a quadrilateral OABC [O(0,0), A(300,0), B(270,30) and C(0,120)] for the inequalities given by constraints 1, 2, 3 and 4 above.

So the solution is any point within this quadrilateral.

However maximum revenue is the farthest point, which is the intersection point of the two lines at (270, 30).

Thus the solution is Produce 270 numbers of Traveler and 30 numbers of Tourer.

The maximum revenue is $72000.

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