You invest in a new play. The cost includes an overhead of $17,500, plus production costs of $2500 per performance. A sold-out performance brings in $3125. (In solving this exercise, let x represent the number of sold-out performances.)
Let x represent the number of sold-out performances.
The production costs for x performances would be 2500 * x.
The revenue earned from x sold-out performances would be 3125 * x.
The total cost of the play would be the sum of the overhead and production costs, which is 17500 + 2500 * x.
The profit from the play would be the revenue minus the total cost, which is 3125 * x - (17500 + 2500 * x).
Simplifying the expression gives you:
Profit = 3125x - 17500 - 2500x
Combining like terms gives you:
Profit = 625x - 17500
To calculate the total profit from the investment in the new play, follow these steps:
Step 1: Calculate the total production costs.
Since the production costs are $2500 per performance and we have x sold-out performances, the total production costs can be calculated as follows:
Total production costs = $2500 * x
Step 2: Calculate the total income from the sold-out performances.
Since a sold-out performance brings in $3125 and we have x sold-out performances, the total income from the sold-out performances can be calculated as follows:
Total income = $3125 * x
Step 3: Calculate the total cost.
The total cost includes the overhead of $17,500 and the total production costs. Therefore, the total cost can be calculated as follows:
Total cost = $17,500 + Total production costs
Step 4: Calculate the total profit.
The total profit is equal to the total income minus the total cost. Therefore, the total profit can be calculated as follows:
Total profit = Total income - Total cost
To summarize:
Total production costs = $2500 * x
Total income = $3125 * x
Total cost = $17,500 + Total production costs
Total profit = Total income - Total cost
To find the profit or loss from investing in the new play, we need to subtract the total cost from the total revenue.
The total cost is the sum of the overhead cost and the production cost per performance:
Total cost = Overhead cost + (Production cost per performance * Number of sold-out performances)
Total cost = $17,500 + ($2500 * x)
The total revenue is the product of the ticket price per sold-out performance and the number of sold-out performances:
Total revenue = Ticket price per sold-out performance * Number of sold-out performances
Total revenue = $3,125 * x
To find the profit or loss, we subtract the total cost from the total revenue:
Profit or loss = Total revenue - Total cost
Profit or loss = ($3,125 * x) - ($17,500 + ($2500 * x))
Simplifying the expression by distributing the multiplication:
Profit or loss = $3,125x - $17,500 - $2,500x
Combining like terms:
Profit or loss = $625x - $17,500
This equation represents the profit or loss in terms of the number of sold-out performances. To find the actual profit or loss, you need to substitute the value of x (the number of sold-out performances) into the equation and evaluate it.