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 store manager is interested in maximizing profits but there are several conditions to consider.

One of these is the space to hold the inventory. The store has $500$ sq$.$ ft$.$ of space. An adult$$s bike needs two sq$.$ ft$.,$ but a child$$s bike needs only one sq$.$ ft$.$

There are $1200$ hours of assembly time available. The girl$$s Sea Sprite and the boy$$s Trail Blazer each needs $4$ hours of assembly time; the Open Trail needs $5$ hours and the Cityscape needs $6$ hours per bike.

The store has specified that at least $35\%$ but not more than $70\%$ of the total order should consist of adult bikes.

Furthermore, the manager wants to make sure that at least $275$ bikes are ordered.

a$.$ Solve a Linear Programming problem to determine how many bikes of each model should be ordered so that the store can make the highest profit.

$)$ b$.$ Use the Sensitivity Report of Excel Solver to answer the following questions.

Recommend a strategy that will help the store increase profits.

Recommend a strategy that will help the store increase variety in the order mix.