Keedy T.
asked • 05/03/14Linear 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?
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2 Answers By Expert Tutors
Parviz F. answered • 05/03/14
Tutor
4.8
(4)
Mathematics professor at Community Colleges
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.
Francisco E.
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.
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05/03/14
Parviz F.
Production of Tourists more than 30 , requires more time than 360 hrs
260 * 200 + 40 Tourists
Time : 260 * 1hr + 40 * 3 hr = 380 hrs.
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05/04/14
Francisco E.
I totally agree with your answer now, the production what was one of the questions is 270 Common or traveler and 30 Touristers.
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05/04/14
Francisco E. answered • 05/03/14
Tutor
5
(1)
Francisco; Civil Engineering, Math., Science, Spanish, Computers.
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.
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Dr Vishwas P.
This is a linear programming problem and needs to work as follows: Let x = number of traveler model and y = number of tourister model to manufacture to maximize revenue. The formulation of the LPP is: Max R = 200x + 600y subject to x + 3y <= 360, x + y <= 300, x >= 0 and y >= 0 The feasible region is a bounded space with vertices at O(0, 0), A(0, 120), B(270, 30) and C(300, 0). The revenue function at these corners are 0, 72000, 72000 and 60000 dollars respectively. The revenue is maximum at both A and B as the revenue function is parallel to x + 3y = 360. Max R = $72000 when the company manufactures (i) no traveler and 120 tourister cycles or (ii) 270 traveler and 30 tourister cycles.02/12/23