For the first question, one has the first find out the min number of months it takes to earn at least 70,000 pounds.

The answer is shown to be x must be less or equal to 30months, where x = number of months.

Risk is taken to be the function 100%-x% , since x must be less or equal to 30, following the math, the minimum risk is 70%. The risk is either 70% or greater.

As to how I would ship the poppies, I would use the function of : probability of success * amt earned. This gives the amount earned when weighed with the risk. The objective is to find the greatest amount, and the number of months that will give the greatest amount.

The function is observed to be y= x/100 * (100-x)
Which is simplified to y= x – (x^2)/100. Where y is the probability*money earned. By either plotting a graph or mere inspection, the highest value of y is 25 when x is 50. Hence the best month to send the 1000 tonnes is after the 50th month.

Part 2: now, if the I ship 1000tons on the 50th month, y= 37,500 according to the working shown. Which is (probability of success * price) + (probability of failure* price/2) .

To find the best chance of earning the most money, a new function is formed and simplified.
It is found to be y=50- (x^2/200)

Using a graph, or in this case differentiation, we find the max value of y to be when x = 0 , thus I would ship all my poppies on the 0th Month for maximum earnings.