he following is a cost function for clinic visits in a small inner city clinic:
Quantity of Visits Total Cost per Week
0 $10
1 15
2 25
3 45
4 75
5 115
6 165
If the price per visit is given to be $25, at what level of visits will the maximum profit position be? What are the profits at this level? What is the quantity supplied?
To find the level of visits that will result in the maximum profit, we need to calculate the profit for each level of visits and identify the level at which the profit is maximum.
To calculate the profit, we need to subtract the cost per visit from the revenue generated. Revenue is equal to the price per visit multiplied by the quantity of visits.
Let's calculate the profit for each level of visits:
Quantity of Visits | Total Cost per Week | Revenue (Price * Visits) | Profit (Revenue - Cost)
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0 | $10 | $0 | -$10
1 | $15 | $25 | $10
2 | $25 | $50 | $25
3 | $45 | $75 | $30
4 | $75 | $100 | $25
5 | $115 | $125 | $10
6 | $165 | $150 | -$15
From the profit calculation, we can see that the profit is maximum at 3 visits, with a profit of $30.
The quantity supplied refers to the quantity of visits that the clinic is able and willing to provide at a given price. In this case, the quantity supplied is equal to the level of visits, which is 3.
Therefore, at the level of 3 visits, the maximum profit position is achieved, with profits of $30, and the quantity supplied is also 3 visits.