Answer and Step-by-step explanation:
To find the linear function representing the cost C(x) to manufacture x chairs, we can use the given data points:
Point 1: (270 chairs, $8025)
Point 2: (520 chairs, $13650)
We can use the formula for the equation of a line, y = mx + b, where y represents the cost C(x) and x represents the number of chairs manufactured. We need to find the values of m and b to complete the equation.
Step 1: Find the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1)
= ($13650 - $8025) / (520 chairs - 270 chairs)
= $5625 / 250 chairs
= $22.5 per chair
Step 2: Use one of the points and the slope to find the y-intercept (b):
y = mx + b
$8025 = ($22.5 per chair) * (270 chairs) + b
$8025 = $6075 + b
b = $8025 - $6075
b = $1950
Therefore, the linear function representing the cost C(x) to manufacture x chairs is:
C(x) = $22.5x + $1950
Now, let's address the remaining questions:
1. What are the fixed daily costs associated with the manufacturing process, even if no chairs are made?
The fixed daily costs associated with the manufacturing process can be determined by identifying the y-intercept (b) in the linear function. In this case, the fixed daily costs are $1950.
2. How much does it cost to make each chair, aside from the fixed costs?
To determine the cost per chair aside from the fixed costs, we can find the coefficient of x in the linear function. In this case, the cost per chair is $22.5.
In summary:
- The fixed daily costs associated with the manufacturing process are $1950.
- The cost to make each chair, aside from the fixed costs, is $22.5.