A fair coin just means 50% heads 50% tails. so the sample is still 50% heads 50% tails.
We are given with the formula
p = 200k - 500
a) The constraint for this formula is obtained from the idea that the profit must be positive
200k - 500 > 0
k > 500/200
k > 2.5
b) To make 14000 profit
14000 = 200k - 500
k = 72.5 or 73 knives must be sold
Divide 6000 by 20
= 300 programs for each perfomance