Question
The manager of a furniture factory finds that it costs $2,200 to manufacture 100 chairs in one day and $4,800 to produce 300 chairs in one day. In reference to this information, answer the following questions: - Assuming that the relationship between cost and the number of chairs produced is linear, find an equation that expresses this relationship. -. What is the slope of the line, and what does it represent? and What is the intersection point and of this line, how is it interpreted? -. If the number of chairs produced in one day is 220, what is the cost?
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Answer to a math question The manager of a furniture factory finds that it costs $2,200 to manufacture 100 chairs in one day and $4,800 to produce 300 chairs in one day. In reference to this information, answer the following questions: - Assuming that the relationship between cost and the number of chairs produced is linear, find an equation that expresses this relationship. -. What is the slope of the line, and what does it represent? and What is the intersection point and of this line, how is it interpreted? -. If the number of chairs produced in one day is 220, what is the cost?
Clarabelle
4.772 Answers
First, calculate the slope \( m \):
m = \frac{4800 - 2200}{300 - 100}
m = \frac{2600}{200}
m = 13
Next, determine the y-intercept \( b \) using the point \( (100, 2200) \):
b = 2200 - 13 \times 100
b = 2200 - 1300
b = 900
Thus, the linear equation is:
C = 13x + 900
The slope \( m = 13 \) represents the cost increase per additional chair produced. The intersection point (0, 900) means that the base cost when no chairs are produced is $900.
Finally, to find the cost for producing 220 chairs, substitute \( x = 220 \):
C = 13 \times 220 + 900
C = 2860 + 900
C = 3860
Therefore, the cost to produce 220 chairs in one day is:
C = 3860
Next, determine the y-intercept \( b \) using the point \( (100, 2200) \):
Thus, the linear equation is:
The slope \( m = 13 \) represents the cost increase per additional chair produced. The intersection point (0, 900) means that the base cost when no chairs are produced is $900.
Finally, to find the cost for producing 220 chairs, substitute \( x = 220 \):
Therefore, the cost to produce 220 chairs in one day is:
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