Otto Toyom builds toy cars and toy trucks. Each car needs 4 wheels, 2 seats, and 1 gas tank. Each truck needs 6 wheels, 1 seat, and 3 gas tanks. His storeroom has 36 wheels, 14 seats, and 15 gas tanks. He needs to decide how many cars and trucks to build so he can maximize the amount of money he makes when he sells them. He makes $1.00 on each car and $1.00 on each truck he sells. (This is a very, very small business, but the ideas are similar for much larger enterprises.) We will divide this problem into subproblems. a) Otto's first task is to figure out what his options are. For example, he could decide to make no cars and no trucks and just keep his supplies. On the other hand, because he likes to make trucks better, he may be thinking about making five trucks and one car. Would this be possible? Why or why not? What are all the possible numbers of cars and trucks he can build, given his limited supplies? This will be quite a long list. An easy way to keep your list organized and find some patterns is to plot the points that represent the pairs of numbers in your list directly on graph paper. Use the x–axis for cars and the y–axis for trucks. Make a fairly large, neat first quadrant graph. (Why the first quadrant?) We will need to use this graph later in this problem and in the next one. b)In part (a) you figured out all the possible combinations of numbers of cars and trucks Otto could make. Which of these give him the greatest profit? Explain how you know your answer is right. You have to convince Otto, who likes trucks better. c) New scenario: Truck drivers have just become popular because of a new TV series called "Big Red Ed. " Toy trucks are a hot item. Otto can now make $2.00 per truck though he still gets $1.00 per car. He has hired you as a consultant to advise him, and your salary is a percentage of the total profits. What is his best choice for the number of cars and the number of trucks to make now? How can you be sure? Explain.