A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: the adult O
Posted: Tue Nov 16, 2021 7:33 am
A large sporting goods store is placing an order for bicycles
with its supplier. Four 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. One of these is 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. 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. The store would like to place an order for at least 275
bikes.
a. Formulate a model
for this problem.
b. Solve your model
with any computer package available to you.
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?
Please take a picture of all your hand writings and the detail
of your work and upload here.
with its supplier. Four 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. One of these is 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. 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. The store would like to place an order for at least 275
bikes.
a. Formulate a model
for this problem.
b. Solve your model
with any computer package available to you.
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?
Please take a picture of all your hand writings and the detail
of your work and upload here.