Final answer:
To calculate the quantity that should be produced in order to maximize profit, we need to find the point where total revenue exceeds total cost by the largest amount. The formula for total revenue is p * q, where p is the selling price and q is the quantity sold. The formula for total cost is $500 + $9 * q, where $500 represents the overhead cost and $9 represents the cost per shirt made. By finding the quantity at which total revenue exceeds total cost by the largest amount, we can determine the quantity that should be produced to maximize profit.
Step-by-step explanation:
To calculate the quantity that should be produced in order to maximize profit, we need to find the point where total revenue exceeds total cost by the largest amount. In this case, the profit-maximizing output level can be determined by comparing the total revenue and total cost. The formula for total revenue is p * q, where p is the selling price and q is the quantity sold.
The formula for total cost is $500 + $9 * q, where $500 represents the overhead cost and $9 represents the cost per shirt made. By finding the quantity at which total revenue exceeds total cost by the largest amount, we can determine the quantity that should be produced to maximize profit.
In this case, the selling price p = 30 - 0.2 √ q. We can substitute this into the formula for total revenue to get an equation for total revenue in terms of q. Then, we can substitute this equation into the formula for total cost to get an equation for total cost in terms of q. By comparing the equations for total revenue and total cost, we can find the quantity at which total revenue exceeds total cost by the largest amount, which will give us the quantity that should be produced to maximize profit.