Linear programming $($Production Planning$)$

BAYNOUNA, Inc. is a company that produces two products, bicycle model A and bicycle model B$,$ over a three$-$month planning horizon$$January$,$ February, and March. The goal is to meet forecasted demand for both products each month while minimizing total production and maintenance costs. Forecasted demand for product bicycle model A is $700$ units in January, $900$ in February, and $1000$ in March, totaling $2600$ units. For product bicycle model B$,$ the forecasted demand is $800$ units in January, $600$ in February, and $900$ in March, totaling $2300$ units. The initial stock is $100$ units of product bicycle model A and $120$ units of product bicycle model B$,$ and a minimum ending stock of $130$ units for product bicycle model A and $110$ units for product bicycle model B is required. Production costs are $20$ per unit for product bicycle model A and $25$ per unit for product bicycle model B$,$ with a maintenance cost of $2\%$ of the production cost per unit each period. The production is constrained by resource availability: machine hours and man$-$hours, with monthly capacities and specific requirements per unit produced. Machine capacities are $3000$ hours in January, $2800$ in February, and $3600$ in March, while available man$-$hours are $2500,2300,$ and $2400$ for the three respective months. Each unit of product bicycle model A requires $1\mathrm{.}5$ machine hours and $1\mathrm{.}1$ man$-$hours, while each unit of product bicycle model B requires $1\mathrm{.}6$ machine hours and $1\mathrm{.}2$ man$-$hours. The objective is to minimize costs subject to demand satisfaction, stock requirements, and resource constraints. Use Linear Programming for modeling this problem.

Managerial Report: Perform an analysis to BAYNOUNA, Inc. case, and prepare a report that summarizes your findings and recommendations. Include the following items in your report: $1.$ Identify the problem in the BAYNOUNA, Inc. Case using the available information. $2.$ What are the key assumptions surrounding the business situation in this case? $3.$ Develop the LP model for this problem. $4.$ Solve the LP model to find the optimal solution. What is the corresponding value of the objective function? $5.$ Analyze the results. $6.$ Include the details of your analysis $($using QM for Windows or Excel QM$)$