A car rental agency has a budgetof $1.8 million to purchase at most 100 new cars. Theagency will purchase either compact cars at $15,000each or luxury cars at $30,000 each. From past rentalpatterns, the agency decides to purchase at most 50 luxurycars and expects an annual profit of $7500 per compactcar and $11,000 per luxury car. How many of eachtype of car should be purchased in order to obtain themaximum profit while satisfying budgetary and otherplanning constraints? Find the maximum profit.