Answer the following question. Formulate as a linear programming (LP) problem

1. Eagle Packaging Inc. (EPI) produces medium and large packaging boxes. Each medium packaging box requires 9 square feet of cardboard, while each large packaging box requires 12 square feet of cardboard. Cardboard is limited to 150,000 square feet daily. Each box must pass through three departments during the production process. The departments are cutting, printing, and assembly departments. In the cutting department, each medium box requires 0.02 labor hour and each large box requires 0.03 labor hours. In the printing department, each medium box requires 0.04 labor hour and each large box requires 0.05 labor hours. In the assembly department, each box requires 0.09 labor hour regardless of size of box. Presently, cutting department has a maximum of 44 labor hours daily, printing department has a maximum of 65 labor hours daily, and assembly department has a maximum of 122 labor hours daily that can be assigned to the production of the two types of boxes. Due to warehouse limitations, no more than 800 large boxes can be made each day. Also, due to customer demand, at least 55 medium boxes must be produced. Medium boxes yield a profit of $14 each, and large ones yield $23 profit each. Formulate this problem as a linear programming (LP) model, to determine the number of each type of packaging box to produce daily, that will maximize profit for EPI. (Only LP formulation is asked for, following the three steps discussed in the slides and course textbook.)