Question - The Diamond Jubilee is a floating riverboat casino that operates on the Mississippi River. The casino is open 24 hours daily and features slot machines, blackjack tables, poker tables, craps tables, and roulette tables. On average, for every $1.00 wagered at the Diamond Jubilee $0.82 goes back to the gamblers as winnings, and $0.08 covers the casino's variable costs. The remaining $0.10 goes toward covering the casino's fixed costs and contributing toward profit. The Diamond Jubilee's fixed costs amount to $27,500 per month, and the casino pays combined state and federal taxes equal to 25% of profit before taxes.
For motivational purposes, the Diamond Jubilee links some of its general manager's compensation to the casino's profitability. Specifically, the riverboat's general manager, Sapphire Sally, receives a monthly bonus equal to 5% of the casino's profit before taxes and any bonus. The bonus is deductible for tax purposes. That is, taxes are paid on post-bonus profit.
How much do Diamond Jubilee patrons have to wager in a month for the casino to earn an after-tax and after-bonus profit of $28,500? (Hint: Begin by writing down the profit equation for pre-tax profit. Add in the bonus payment. Expand to consider taxes.)