Arrera Automobiles, the first Albanian automobile manufacturing company, organizes the vehicles it manufactures into three families: a family of trucks, a family of small cars, and a family of midsized and luxury cars. One plant outside Tirana, Albania assembles two models from the family of midsized and luxury cars. The first model, Illyrian Pure, is a four-door sedan with vinyl seats, plastic interior, standard features, and excellent gas mileage. It is marketed as a smart buy for middle-class families with tight budgets, and each Illyrian Pure sold generates a modest profit of $3,600 for the company.

The second model, the Illyrian Sport, is a two-door luxury sedan with leather seats, wooden interior, custom features, and navigational capabilities. It is marketed as a privilege of affluence for upper middle-class families, and each Illyrian Sport sold generates a healthy profit of $5,400 for the company. Agron, the manager of the assembly plant, is currently deciding the production schedule for the next month. Specifically, he must decide how many Illyrian Pure and how many Illyrian Sports to assemble in the plant to maximize profit for the company. He knows that the plant possesses a capacity of 48,000 labor-hours during the month. He also knows that it takes 6 labor-hours to assemble one Illyrian Pure and 10.5 labor-hours to assemble one Illyrian Sport.

Because the plant is simply an assembly plant, the parts required to assemble the two models are not produced at the plant. They are instead shipped from other plants around the Tirana area to the assembly plant. For example, tires, steering wheels, windows, seats, and doors all arrive from various supplier plants. For the next month, Agron knows that he will be able to obtain only 20,000 doors (10,000 left-hand doors and 10,000 right-hand doors) from the door supplier. A recent labor strike forced the shutdown of that particular supplier plant for several days, and that plant will not be able to meet its production schedule for the next month. Both the Illyrian Pure and the Illyrian Sport use the same door part.

In addition, a recent company forecast of the monthly demands for different automobile models suggests that the demand for the Illyrian Sport is limited to 3,500 cars. There is no limit on the demand for the Illyrian Pure within the capacity limits of the assembly plant.

Formulate a linear programming model for the problem. Solve through Excel Solver to determine the number of Illyrian Pure and the number of Illyrian Sports that should be assembled