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 an LP model for this problem, including variables, OF & constraints.
b. Solve said model with Lingo computer package. Discuss the solution printout.
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 could have 100 more feet of storage space?
e. If profit on the Cityscape increases to $35, how many Cityscape bikes are ordered?