b. (2 marks) A company does $100 million in sales. It has some degree of pricing power in that it

sells its output for $10 where it costs it $8 to make. Its advertising is highly effective. For every

one percent it increases its advertising budget, its output increases by five percent. Unfortunately,

its advertising is very aggressive because it causes its competitors to increase theirs by two

percent for every one percent the company increases its own. When its competitors increase their

budgets by one percent, it causes problems for the company in that demand for its output falls by

two percent. Calculate how much, in dollars, the company should spend on advertising.

c. (2 marks) Consider a team in the bottom league where its probability of promotion to the top

league is equal to pT = w, its total cost is given by C = 200+100w and demand is given by

P = 200125w. It is expected that it can earn $130 million in the top league next year but only

$20 million if it remains in the bottom league next year. It uses a discount rate of r = 0.1 (ie, 10

percent). Calculate its optimal winning percentage this year.

d. (2 marks) A big Las Vegas casino expects that, for an upcoming UFC match, 50 percent of the

money wagered will be placed on Connor MacGregor winning, 40 percent of the money will be

bet on Dustin Pear Tree winning and 10 percent of the money will be bet on a draw. If the casino

wants to guarantee a profit of $0.20 on every $1 bet, what should it set the odds at for each

outcome? (You may use British, European or American odds for your answer.)