4. An automobile company produces three different models of a popular vehicle, a sports model, an economy model, and a luxury model and wants to maximize profits. The company makes a profit of $1,500 for each sports model, $750 for each economy model, and $2,250 for each luxury model. The company can't make more than a total of 2,000 vehicles. The company also wants to make at least 200 sports models, at least 500 economy models, and at least 300 luxury models.

a) Define the decision variables.

b) Write the objective function.

c) Write the constraints in standard form.