The Powerball lottery is open to participants across several states. When entering the powerball lottery, a participant selects
five numbers from 1-59 and then selects a powerball number from the digits 1-35. In addition, there’s a $1 million payoff for anybody selecting the first five numbers correctly. • Show that the odds of winning the Powerball Jackpot are 1 in 175, 223, 510. • Show that the odds of winning the $1 million are 1 in 5, 153, 632. On February 18, 2006 the Jackpot reached $365 million. Assuming that you will either win the Jackpot or the $1 million prize, what’s your expected value of winning? Mega Millions is a similar lottery where you pick 5 balls out of 56 and a powerball from 46. Show that the odds of winning mega millions are higher than the Powerball lottery On March 30, 2012 the Jackpot reached $656 million. Is your expected value higher or lower than that calculated for the Powerball lottery?
1 answer:
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Answer:
The oranges should be picked in 2 weeks for maximum return
Explanation:
We assume that the return of the owner is y ($)
Assume that the number of weeks the oranges should be picked to have maximum return is x (weeks). (x≥0)
If collect now, the price for each bushel is $27
As the price per bushel decrease by $1.50 per bushel each week
=> After x weeks, the price of a bushel decrease: 1.5x ($)
=> The price of 1 bushel after x weeks is: 27 - 1.5x ($)
If collect now, each tree can yield 7 bushels
As the yield increases by half a bushel per week for the next 5 weeks
=> After x weeks with x ≤ 5, each trees would yields: 7 + 0.5x (bushels)
The return = The price of each bushes × The quantity of bushels
=>
⇔
⇔
We have: if the equation has the form of with a≠0, its maximum value is:
In the equation , we have: a = -0.75; b = 3; c = 189
=>
To look for the number of weeks, we should find x (0≤x≤5) with which y = 192
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⇔
⇔
⇔
⇔ x = 2
The oranges should be picked in 2 weeks for maximum return