6 Part III. Problem Solving (40 points, 20 each): Show all your steps to earn partial credits. At most two points may be given to correct answer without essential work shown: (1) (Spring Break-Minimizing cost, 20 points) The student activities department of a college plans to rent buses and vans for a spring-break trip. Each bus has 48 regular seats and 2 handicapped seat; each van has 8 regular seat and 3 handicapped seats. The rental cost is $350 for each van and $975 for each bus. If 480 regular and 36 handicapped seats are required for the trip, how many vehicles of each type should be rented to minimize cost? What is the min cost? (a) Make a chart to illustrate the problem, using x= number of buses and y = Number of vans to be rented. (b) Set up a linear programming problem - an objective function and a system of inequalities (c) Graph the solution region R of the system of linear inequalities and find its corner points. (d) Calculate the values of the objective function at all corner points and put your answer to the questions in plain English