A large sporting goods store is placing an order for bicycles with its supplier. Four types of models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The LP model should maximize profit.

There are several conditions that the store needs to worry about:

The first constraint is about space to hold the inventory. An adult's bike needs two feet, but a child's bike needs only one foot. The store has 500 feet of space.

The second constraint is about availability of assembly time. There are 1200 hours of assembly time available. The child's bike need 4 hours of assembly time; the Open Trail needs 5 hours and the Cityscape needs 6 hours.

As the third constraint, the store would like to place an order for at least 275 bikes.

a. Formulate an LP model for this problem. (by ignoring the integer requirements for decision variables)

b. Solve your model with Excel Solver.

c. How many of each kind of bike should be ordered and what will the profit be?

d. What would the profit be if the store had 100 more feet of storage space?

e. If the profit on the Cityscape increases to $35, will any of the Cityscape bikes be ordered?

f. Over what range of assembly hours is the dual price applicable?

g. If we require 5 more bikes in inventory, what will happen to the value of the optimal solution?

h. Which resource should the company work to increase, inventory space or assembly time?
Transcribed Image Text:A large sporting goods store is placing an order for bicycles with its supplier. Four types of models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The LP model should maximize profit. There are several conditions that the store needs to worry about: • The first constraint is about space to hold the inventory. An adult's bike needs two feet, but a child's bike needs only one foot. The store has 500 feet of space. • The second constraint is about availability of assembly time. There are 1200 hours of assembly time available. The child's bike need 4 hours of assembly time; the Open Trail needs 5 hours and the Cityscape needs 6 hours. • As the third constraint, the store would like to place an order for at least 275 bikes. a. Formulate an LP model for this problem. (by ignoring the integer requirements for decision variables) b. Solve your model with Excel Solver. c. How many of each kind of bike should be ordered and what will the profit be? d. What would the profit be if the store had 100 more feet of storage space? e. If the profit on the Cityscape increases to $35, will any of the Cityscape bikes be ordered? f. Over what range of assembly hours is the dual price applicable? g. If we require 5 more bikes in inventory, what will happen to the value of the optimal solution? h. Which resource should the company work to increase, inventory space or assembly time?

Name: A large sporting goods store is placing an order for bicycles with its
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: A large sporting goods store is placing an order for bicycles with its supplier. Four types of models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered

Question

A large sporting goods store is placing an order for bicycles with its supplier. Four types of models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The LP model should maximize profit.

There are several conditions that the store needs to worry about:

The first constraint is about space to hold the inventory. An adult's bike needs two feet, but a child's bike needs only one foot. The store has 500 feet of space.
The second constraint is about availability of assembly time. There are 1200 hours of assembly time available. The child's bike need 4 hours of assembly time; the Open Trail needs 5 hours and the Cityscape needs 6 hours.
As the third constraint, the store would like to place an order for at least 275 bikes.

a. Formulate an LP model for this problem. (by ignoring the integer requirements for decision variables)

b. Solve your model with Excel Solver.

c. How many of each kind of bike should be ordered and what will the profit be?

d. What would the profit be if the store had 100 more feet of storage space?

e. If the profit on the Cityscape increases to $35, will any of the Cityscape bikes be ordered?

f. Over what range of assembly hours is the dual price applicable?

g. If we require 5 more bikes in inventory, what will happen to the value of the optimal solution?

h. Which resource should the company work to increase, inventory space or assembly time?

A large sporting goods store is placing an order for bicycles with its supplier. Four types of models can be ordered: the adult Open Trail,
the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits,
respectively, are 30, 25, 22, and 20. The LP model should maximize profit.
There are several conditions that the store needs to worry about:
• The first constraint is about space to hold the inventory. An adult's bike needs two feet, but a child's bike needs only one foot. The store
has 500 feet of space.
• The second constraint is about availability of assembly time. There are 1200 hours of assembly time available. The child's bike need 4
hours of assembly time; the Open Trail needs 5 hours and the Cityscape needs 6 hours.
• As the third constraint, the store would like to place an order for at least 275 bikes.
a. Formulate an LP model for this problem. (by ignoring the integer requirements for decision variables)
b. Solve your model with Excel Solver.
c. How many of each kind of bike should be ordered and what will the profit be?
d. What would the profit be if the store had 100 more feet of storage space?
e. If the profit on the Cityscape increases to $35, will any of the Cityscape bikes be ordered?
f. Over what range of assembly hours is the dual price applicable?
g. If we require 5 more bikes in inventory, what will happen to the value of the optimal solution?
h. Which resource should the company work to increase, inventory space or assembly time?

Accepted Answer

a let, x1=number of adult open trail bicycles ordered 
  x2=number of adult cityscape bicycles…