One Word Document with a report outlining your recommendations for the issues $($i$.$e$.$ decisions$)$ listed in the case. The document should also include an appendix for each of the issues showing your decision variables, algebraic equations, and a readable screen clip of your excel output, including the solver dialogue box $($see parts a and b below$).$ It is especially important to show how you used solver.

One Excel Spreadsheet with clearly labeled worksheets $($one worksheet for each of the issues in the assignment$).$ The work in each worksheet needs to be well organized and clearly labeled, with formulas used appropriately.

The general approach for solving each of the issues should be:

a$.$ Formulate the linear programming model for the issue algehraically. Group this into three sections: $1)$ Definition of Decision Variables, $2)$ Objective Function Equation, and $3)$ Constraints Equations. This should go in the appendix of your report$/$memo$.(6$ marks for each issue$)$

b$.$ Set up and solve this problem using excel. Include screenshots of this in the appendix to the report$/$memo$.(8$ marks for each issue$)$

c$.$ Provide your answers and recommendations to the manager of the company $($include your recommendations for all issues in a single report$/$memo$).$ See the basic structure of the report or memo on pages $3$ & $4.(2$ marks for each issue$)$

d$.$ General organization and formatting $(4$ marks$)$

MGTS $113$ Linear Programming Group Assignment $-$ Winter $2024$

Decision $1$: Product Mix

Penny Chairs received financing from Funance Inc. to produce three types of atdoor chairs that are ideally suited to the beach, pool, and patios: sling chairs, Adirondack chairs, and hammocks. At its Bruderheim factory, the unit profit for these chairs is $$40,$$$100,$ and $$90$ respectively. Additionally, each type of chair requires cutting, assembly, and finishing. Workers cannot spend more than $50$ hours per month on any one activity $($i$.$e$.$ cutting, assembly, and finishing$).$ Sling chairs are made up of ten wood pieces for the frame and one piece of cloth. The cutting of the wood takes $30$ minutes. Assembly includes sewing the cloth and the attachment of rivets, screws, and fabric. This takes $45$ minutes per chair. The finishing step involves sanding, staining, and varnishing chair parts and takes one hour per chair. Adirondack chairs take two hours for the cutting phase as well as the assembly phase whereas the finishing stage takes one hour. For a hammock, cutting takes $0\mathrm{.}4$ hours, assembly takes three hours, and finishing takes one hour.

a$)$ Penny Chairs wants to determine the appropriate product mix at their Bruderheim factory in order to maximize profit. Which constraints are binding? Why?

b$)$ Penny Chairs has utilized $Al$ to reduce all of the above times by $10\%$ but the $Al$ program license will cost $$300$ per month. Should they implement the Al program?