Instructions: Electronically submit your answers to Canvas by the due date. For Parts $($a$)$ and $($c$),$ type your solution in a single Microsoft Word document. For Part $($b$),$ submit your original Excel file and KEEP the formulas in the cells and the solver so we can see your work.

EquiBags makes equipment bags for professional camera equipment, and it offers two models: regular and deluxe. The company has a prior pricing agreement with a distributor willing to buy as much of each bag as it can make. There are three steps in making a bag: cutting, sewing, and finishing. Each regular bag requires $1$ hour of cutting, $1\mathrm{.}25$ hours of sewing, and $0\mathrm{.}75$ hours of finishing. Each deluxe bag needs $2$ hours in cutting, $1\mathrm{.}75$ hours in sewing, and $0\mathrm{.}5$ hours in finishing. The profit obtained for each regular bag is $$10,$ while for each deluxe bag is $$15.$ The director of manufacturing estimates that $630$ hours for cutting, $600$ hours for sewing, and $708$ hours for finishing will be available during the next production cycle. To maximize profit, the company needs to determine the optimal number of regular and deluxe bags to produce in the next production cycle.

a$)$ Algebraically, formulate a linear programming model that determines the optimal number of regular and deluxe bags that EquiBags needs to produce in the next production cycle. $(10$ points$)$

Hint: Carefully define each decision variable $($be very specific about variables!$).$ Review the Flair Furniture example posted on Canvas along with this assignment.

b$)$ Formulate your linear program in Excel and use the Solver to solve it$.(10$ points$)$

Hint: Review the Excel formulation for the Flair Furniture example and watch the video posted on Canvas if you need further help.

c$)$ Should EquiBags hire more employees to increase its finishing capacity? Why? How about the sewing capacity? Why? $(5$ points$)$