A renowned electronics retailer is stocking up on smart devices with its supplier. Four innovative models

are available for ordering: the Smart Home Hub, the Portable Speaker, the Wearable Fitness Tracker, and

the Virtual Reality Headset. It is anticipated that every product ordered will find a happy buyer, with

profits of $$30,$ $$25,$ $$22,$ and $$20$ respectively. However, the retailer must navigate through several

considerations. Among these, space constraints for storing inventory are paramount. The Smart Home

Hub requires two square feet of storage, while the Wearable Fitness Tracker requires only one square

foot. Thankfully, the retailer has a total of $500$ square feet $6$available. Additionally, there's the matter of

assembly time. With $1200$ hours at their disposal, the assembly team can work diligently. The Wearable

Fitness Tracker necessitates $4$ hours of assembly time, while the Smart Home Hub requires $5$ hours, and

the Portable Speaker demands $6$ hours. Despite these constraints, the retailer is eager to fulfill the needs

of its tech$-$savvy customers. They aim to place an order for no less than $275$ smart devices to keep up

with the ever$-$evolving demand. The objective of the company is to maximize profit.

a$.$ Developed and write a mathematical model by identifying suitable decision variables,

objective function constraints etc.

b$.$ Solve your model with LINGO and provide your answer on how many of each kind of

bike should be ordered by store, and what the profit will be$.$

c$.$ What would the profit be if the store had $100$ more feet of storage space? Explain your

answer with reason.

d$.$ Which resource should the company work to increase and how much i$.$e$.$ inventory space

or assembly time to get more profits? How you selected the answer, explain.