To plot the relationship between cost and the number of bottles produced:
Step 1: Define the axes.
• The horizontal axis (x-axis) represents the Number of Bottles Produced (x).
• The vertical axis (y-axis) represents Total Cost (₦) (C(x)).
Step 2: Identify the Cost Function.
The cost function is given by:
C(x)=10,000+0.03x
Step 3: Calculate two points for the line.
• Point 1 (Y-intercept - Fixed Cost): When no bottles are produced (x=0), the cost is the fixed cost.
C(0)=10,000+0.03×0=10,000
Plot the point (0,10,000).
• Point 2 (Cost at Maximum Annual Capacity): The annual capacity is 600,000 bottles.
C(600,000)=10,000+0.03×600,000
C(600,000)=10,000+18,000
C(600,000)=28,000
Plot the point (600,000,28,000).
Step 4: Draw the graph.
• Draw a straight line connecting the two points: (0,10,000) and (600,000,28,000).
• This line represents the total cost of producing different quantities of bottles, up to the annual capacity.
Description of the Graph:
The graph will be a straight line that starts at ₦10,000 on the vertical axis (representing the fixed cost) and slopes upwards. As the number of bottles produced increases along the horizontal axis, the total cost increases linearly along the vertical axis.