Problem 1: A businessman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 96,000 cu. ft. Three types of trucks are appropriate for the specialized operation. Their characteristics and costs are summarized in the table below. There are 42 potential drivers available and there are facilities for at most 25 trucks. The businessman's objective is to minimize the total cost outlay for trucks. Capacity per Drivers Needed Truck Cost per Truck per Truck Type Truck (Cu.Ft.) Small $20000 2000 1 Medium $30000 4500 2 Large $50000 7000 3 a) Set up the linear programming model (variables, objective function, constraints, etc). 0.75 pt Use Excel to answer the following questions: b) What is the optimal solution? What is the minimum total cost? 0.75 pt c) If the cost of a medium truck is increased by $ABC, where ABC is the last 3 digits of your student ID, what is the new optimal solution and the new optimal total cost? Explain. 0.5 pt d) If the minimum daily trucking capacity is decreased by $ABC, where ABC is the last 3 digits of your student ID, what is the new optimal total cost? Explain. 0.5 pt