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 one hour, while it takes three hours for the Tourister. There are 300 frames and 360 hours of labor available for production. How many of each model should be produced to maximize revenue?

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

Every 3 hours spend on Assembling on a tourists make one sells for $600

During 3 hours of time makes 3 Traveler sells : $200 * 3 = $600

So 360 hours spend anyway income earned per hour is same.

Anyway 360 hour allocated for production same revenue will be obtained is $200 .

200 * 360 = $72000

360/4 =90

Production 90 *3 = 270 Tourists

300 -270=30 Traveler produced

Correction is made

360 should be distributed with the ratio of 3:1

270 , and 30 is the answer

See the table below that if Tourists produced more than 30, then requires more than 360 hrs of work.

First we need to solve two equations to make sure that the constraints are being fulfilled.

C + 3T = 360 hours of labor

C + T = 300 Number of frames

The result is T = 30 units and C = 270 Units. The only answer that gives the maximum income is this and at the same time satisfies the constraints.

The maximum income will be $ 62000.

This answer was checked with solver in Excel.

What are the constraints??

For me the constraints are: 1.- The two bicycles that are sold must add 300 and the other is that The total hours of labor are 360

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