The overhead or fixed cost for the company is 1,000 per week. In addition, the cost of manufacturing each boat costs$200. Find an equation C=f(x) for the total cost per week where x is the number of boats manufactured in a week.
b) Graph the total cost function for 0<x<30
C(x) = 1000 + 200x
To find an equation for the total cost per week, you need to consider both the fixed cost and the variable cost of manufacturing each boat.
The fixed cost is $1,000 per week, which remains constant regardless of the number of boats manufactured. This can be represented as a constant term in the equation.
The variable cost is the cost of manufacturing each boat, which is $200 per boat. The total variable cost depends on the number of boats manufactured, so it can be represented by a linear term in the equation.
Therefore, the equation C=f(x) for the total cost per week can be written as:
C = 1,000 + 200x
Now, let's graph the total cost function for the given range of 0 < x < 30.
To do this, you can plot a graph with "x" on the x-axis representing the number of boats manufactured and "C" on the y-axis representing the total cost per week.
Choose a set of values for x within the given range (0 < x < 30), such as 0, 5, 10, 15, 20, 25, and 30. Plug these values into the equation C = 1,000 + 200x to calculate the corresponding values of C.
For example:
When x = 0, C = 1,000 + 200(0) = 1,000
When x = 5, C = 1,000 + 200(5) = 2,000
When x = 10, C = 1,000 + 200(10) = 3,000
When x = 15, C = 1,000 + 200(15) = 4,000
When x = 20, C = 1,000 + 200(20) = 5,000
When x = 25, C = 1,000 + 200(25) = 6,000
When x = 30, C = 1,000 + 200(30) = 7,000
Plot these points on a graph, with x on the x-axis and C on the y-axis. Connect the points to form a line. The resulting graph will show the total cost function for the range of 0 < x < 30.