a company maufacturing surfboards has fixed costs of $300 per day and total costs of $5100 per day for a daily output of 20 boards. Assume the total cost per day C(x) is linearly related to the total output per day x. write an equation for the cost function, and write an equation for the average cost function Ċ(x)=c(x)/x. what does the average cost per board tend to as production increases (assume production output goes to infinity)?
To find the equation for the cost function, we need to determine the variable cost per unit of output.
The fixed cost is given as $300 per day, which means it remains constant regardless of the number of surfboards produced.
The total cost per day is given as $5100 for a daily output of 20 boards. We can subtract the fixed cost from the total cost to find the variable cost.
Variable Cost = Total Cost - Fixed Cost
Variable Cost = $5100 - $300
Variable Cost = $4800
Since the total cost per day is linearly related to the total output per day, we can express the cost function C(x) as:
C(x) = Variable Cost * x + Fixed Cost
C(x) = $4800x + $300
C(x) = 4800x + 300
To find the equation for the average cost function Ċ(x) = C(x)/x, we can divide the cost function C(x) by the number of boards produced x:
Ċ(x) = (4800x + 300) / x
Ċ(x) = 4800 + 300/x
Now, let's analyze the behavior of the average cost per board as production increases.
In this case, as production output (x) goes to infinity, the value of 300/x tends towards zero. This means that the average cost per board Ċ(x) will approach the constant value of 4800.
So, as production increases indefinitely, the average cost per board for the company will tend towards $4800.