A major automobile manufacture is considering how to allocate a $2 million advertising budget between two types of television program: NFL football games and PGA tour professional golf tournaments. The following table shows the new sport utility vehicles (SUVs) that are sold when a given amount of money is spent on advertising during an NFL football game and a PGA tour golf event. New SUV Sales Generated (thousands of vehicles per year) Total Spent NFL Football PGA Tour Golf (millions) $0.0 0 0 $0.5 10 4 $1.0 15 6 $1.5 19 8 $2.0 20 9 The manufacture's goal is to allocate its $2 million advertising budget to maximize the number of SUVs sold. Let F be the amount of money devoted to advertising on NFL football games, G the amount of money spent on advertising on PGA tour golf event, and Q(F,G) is the number of new vehicles sold. (a) What is the objective function for this problem? (2) (b) What is the constraint? (2) (c) Write a statement of the constrained optimization problem. (2) (d) The following table shows vehicle sales based on all possible combinations of spending on football games and golf events. Complete the following table. (4) New sales from F New sales from G Total new sales (F, G) (0.0, 2.0) (0.5, 1.5) (1.0, 1.0) (1.5, 0.5) (2.0, 0.0) (e) What is the optimal combination of spending on football games and golf events that maximize the number of SUVs sold? (3) What are the maximum sales given the $2 million advertising budget? (2)