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. The store needs to worry about several conditions. 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 bikes 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.

Answer questions $9-15$ based on the ebove information.

Formulate an LP model for this problem.

Assume that $x_1,x_2,x_3,x_4$ are the number of blcycles to be ordered from each category Open Trail, Cityscape, Sea Sprite, and Trall Blazer respectively.