Scenario: The bicycle center also sells new bikes. He purchases three types of b

Question

Scenario: The bicycle center also sells new bikes. He purchases three types of bicycles from manufacturers in kit form, then assembles, services & inspects them prior to sale. The assembly of mountain bikes requires 3.25 hours, cross-country bikes require 2.85 hours and three-wheelers require 4.35 hours of labor. Servicing mountain bikes requires 2.55 hours, cross-country bikes require 1.05 hours and three-wheelers require 3.25 hours of labor. The inspection & testing of mountain bikes requires 2.32 hours, cross-country bikes require 2.75 hours and three-wheelers require 3.1 hours of labor. The center makes a profit of $155.50 on each mountain bike, $131.75 on cross-country bikes and $220.75 on each three-wheeler. The center has 170 assembly hours, 210 service hours and 250 inspection & testing man-hours available. Because spring is just around the corner the center decides that it is best if twelve mountain bikes and eleven cross-country bikes are assembled and stocked ready for sale.

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Question 22: How many mountain bikes should he assemble & stock in his center in order to make the maximum profit? Round down your answer to the nearest whole bike.
Question 23. How many cross-country bikes should he assemble & stock in his center in order to make the maximum profit? Round down your answer to the nearest whole bike.
Question 24. How many three-wheeler bikes should he assemble & stock in his center in order to make the maximum profit? Round down your answer to the nearest whole bike.
Question 25. Using the rounded values for Questions 22 - 24 calculate the maximum profit?

Explanation / Answer

Bike Type -->>>

Decision variables:

Number of Mountain bikes produced: X1

Number of Cross-country bikes produced: X2

Number of Three-wheelers produced: X3

Constraints:

3.25X1+2.85X2+4.35X3<=170
2.55X1+1.05X23.25X3<=210
2.32X1+2.75X1+3.1X3<=250

X1>=12, X2>=11

Objective Function:

Max: Profit 155.5X1+131.75X2+220.75X3

Hope this will be helpful

Thanks and God bless You :-)

Bike Type -->>>

Mountain Bikes Cross-country bikes Three-Wheelers Total hours available Hours of labor for assembly 3.25 2.85 4.35 170 Hours for servicing 2.55 1.05 3.25 210 Inspection and testing 2.32 2.75 3.1 250 Profit each bike 155.5 131.75 220.75

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