Step-by-step explanation:
so, they want to sell 200,000 tickets (and we assume they can really sell all of these).
they have to pay the prize money afterwards :
1 × $8,000 = $8,000
10 × $300 = $3,000
75 × $50 = $3,750
--------------
$14,750
and they have to pay for the ticket production at the beginning.
this is not really well defined, but I assume the following :
C(20) = 4500 + 6x
x = units of 10,000 tickets (because of the functional argument of 20, and we have to deal with 200,000 tickets).
that means the cost for these 200,000 tickets is then
4500 + 6×20 = $4,620
$4,500 are fixed costs insurgent of the number of tickets (like for creating the design, configuring the printing machines for the design, ...).
and 6×20 = $120 are the cost of actuality printing the tickets ($6 per 10,000 ticket prints).
so, the total expenses are
$14,750 + $4,620 = $19,370
under the assumption they can sell all 200,000 tickets to just break even, the prize for each ticket must be
19,370 / 200,000 = $ 0.09685 ≈ $0.10
if my assumptions are wrong, please adapt the numbers in the calculations i showed you here.
for example, what if the x in the printing cost is per ticket and not per 10,000 tickets ?
then the printing costs would be
4500 + 6×200000 = $1,204,500
and the total expenses would be
$14,750 + $1,204,500 = $1,219,250
and the prize per ticket would have to be
1,219,250 / 200,000 = $ 6.09625 ≈ $6.10