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Philadelphia fun-cycles (PFC) is buying new cycles for rentals during the next summer season for tourists visiting Fairmount park. It has a budget of has $180,000 that can be used to purchase new rental cycles that can have 1, 2, or 4 seats.  The cycles can be purchased from two different manufacturers. PFC would like to purchase at least 60 cycles in total. These cycles can be any mix of 1, 2, or 4 seaters. PFC wants a total seating capacity of at least 150. PFC also wants to buy at least 45 one-seaters, 45 two-seaters and 45 four-seaters They would like to purchase the same number of cycles from both manufacturers to maintain goodwill.

Philadelphia fun-cycles (PFC) is buying new cycles for rentals during the next summer season for tourists visiting Fairmount park. It has a budget of has $180,000 that can be used to purchase new rental cycles that can have 1, 2, or 4 seats.  The cycles can be purchased from two different manufacturers. PFC would like to purchase at least 60 cycles in total. These cycles can be any mix of 1, 2, or 4 seaters. PFC wants a total seating capacity of at least 150. PFC also wants to buy at least 45 one-seaters, 45 two-seaters and 45 four-seaters They would like to purchase the same number of cycles from both manufacturers to maintain goodwill.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 93P
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Philadelphia fun-cycles (PFC) is buying new cycles for rentals during the next summer season for tourists visiting Fairmount park. It has a budget of has $180,000 that can be used to purchase new rental cycles that can have 1, 2, or 4 seats.  The cycles can be purchased from two different manufacturers. PFC would like to purchase at least 60 cycles in total. These cycles can be any mix of 1, 2, or 4 seaters. PFC wants a total seating capacity of at least 150. PFC also wants to buy at least 45 one-seaters, 45 two-seaters and 45 four-seaters They would like to purchase the same number of cycles from both manufacturers to maintain goodwill.

 

Cycle

Builder

Cost

Seating

Capacity

Expected Daily Profit

The Roadie

Mighty Cycles

$500

1

$100

The Doubler

Mighty Cycles

$900

2

$140

The Rickshaw

Mighty Cycles

$1800

4

$200

The Speedy

S&K Cycles

$800

1

$115

The Cozy

S&K Cycles

$1000

2

$150

The Caravan

S&K Cycles

$1500

4

$180

 

How many cycles and which type of cycles should PFC purchase? Formulate this problem as a linear program and solve it.

  1. Define the decision variables needed to model this problem.
  2. The objective is to maximize nightly revenue. Give the objection function.
  3. Write the constraints.
  4. What is the final answer? Explain in detail.
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