Discuss the below:
Q: Model Hummer, a toy car manufacturer from South Bend, produces small replicas of Hummer for kids. They are considering offering some combination of two different models-MachoHum and TimidHum. Both are made out of the same environment risk-free Polylactic acid (PLA), a plastic substitute made from fermented plant stare (usually corn). Model Hummer has a long-term contract with a supplier of the plastic substitute and receives a 5000 square--foot shipment of the material each week. Each MachoHum requires 3 square feet while each TimidHum requires 2 square feet. The soles forecasts indicate that at most 1000 MachHums and 1200 TimidHums can be sold per week. Each MachoHum requires 45 minutes of labor to produce and generates a unit profit of $32. Each TimidHum requires 40 minutes of labor and generates o unit profit of $24. Model Hummer has 35 laborers that each provides 40 hours of labor per week. Management wishes to know what quantity of each type of small replicas of Hummer to produce per week.
Formulate a linear programming model algebraically. Write down the objective function, the functional constrain the non-negativity constraints, and draw the graph and show the feasible region.