Question

General tickets sell for $6 and adult $9. Sell at most 300 general and at most 500 adult. Costs $1 to advertise for adult and $.50 to advertise student. Have at most $400 for advertising. What is most profit that can be made?

Answer 1

Cost=.5S+A<=400
Assuming "general" means student in second sentence.
A=-1/2 S + 400

Profit=6S+9A-costs
= 6S+9A-.5S-A
profit= 8A+5.5S
now, looking at the constraints, S,A>0, then the max S is 300, and max A is 400, then the max profit occurs at one of those points...
Profit(A,S):P(400,0)=3200
Profit(0,300)=1650
max profit is 3200, selling all adult tickets. Profit is limited by 400 advertising total cost. If one were able to move that to a total cost of 650, the available profit would be
Profit=500*8+300*5.5=4000+1650=
= 5650 which means for an extra 250 dollars of advertising, one would make an extra 4000 dollars.