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. Define the decision variables, give the objection function, and write the constraints. What is the final answer? Explain in detail.
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.
- Define the decision variables, give the objection function, and write the constraints.
- What is the final answer? Explain in detail.
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