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# Linear Programming Problems

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?

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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
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.

I AGREE WITH YOUR ANSWER BUT THEN, YOU ARE NOT USING THE 300 FRAMES BUT 180+60=240. THIS MAY BE ANOTHER WAY OF LOOKING AT THE PROBLEM. I ASSUMED THAT THE 360 HOURS NEED TO BE CONSUMED AND THE 300 FRAMES AS WELL.
Production of Tourists more than 30 , requires more time than 360 hrs

260 * 200 + 40 Tourists

Time :  260 * 1hr + 40 * 3 hr = 380 hrs.
I totally agree with your answer now, the production what was one of the questions is 270 Common or traveler and  30 Touristers.
Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
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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.