I made a mistake. It should read at most instead of at least.
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?
To find the most profit that can be made, we need to determine the optimal number of general tickets and adult tickets to sell.
Let's assume that the number of general tickets sold is represented by "g" and the number of adult tickets sold is represented by "a". The objective is to maximize profit, which is given by the formula:
Profit = (Revenue from general tickets) + (Revenue from adult tickets) - (Advertising cost)
The revenue from selling general tickets is given by:
Revenue from general tickets = (number of general tickets sold) * (price per general ticket)
Therefore, the revenue from general tickets can be calculated as:
Revenue from general tickets = g * $6
The revenue from selling adult tickets is given by:
Revenue from adult tickets = (number of adult tickets sold) * (price per adult ticket)
Therefore, the revenue from adult tickets can be calculated as:
Revenue from adult tickets = a * $9
The advertising cost is given by:
Advertising cost = (Cost to advertise adult ticket) * (number of adult tickets sold) + (Cost to advertise student ticket) * (number of general tickets sold)
Therefore, the advertising cost can be calculated as:
Advertising cost = ($1 * a) + ($0.50 * g)
Now, let's set the constraints based on the given information:
1. At most 300 general tickets can be sold: g <= 300
2. At most 500 adult tickets can be sold: a <= 500
3. The total advertising cost should not exceed $400: ($1 * a) + ($0.50 * g) <= 400
To find the most profit, we can use linear programming techniques or solve it graphically. Let's solve it graphically:
1. Plot the constraints on a graph.
2. Determine the feasible region where the solutions to all the constraints overlap.
3. Calculate the profit for each coordinate within the feasible region.
4. Find the coordinate(s) that maximize the profit.
By following these steps, you will be able to determine the most profit that can be made based on the given constraints.