50. Manufacturing Cost The manager of a furniture factory finds that it costs $2200 to produce 100 chairs in one day and $4800 to produce 300 chairs in one day. a. Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x chairs in one day. b. Draw a graph of C. What is the slope of this line? c. At what rate does the factory's cost increase for every additional chair produced?
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Given: Cost for 100 chairs = $82,200 Cost for 300 chairs = $84,800 Change in cost = $84,800 - $82,200 = $2,600 Change in number of chairs = 300 - 100 = 200 Slope (m) = Change in cost / Change in number of chairs Slope (m) = $2,600 / 200 Slope (m) = $13 ** Show more…
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The manager of a furniture factory finds that it costs $\$ 2200$ to produce 100 chairs in one day and $\$ 4800$ to produce 300 chairs in one day. a. Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function $C$ that models the cost of producing $x$ chairs in one day. b. Draw a graph of $C$. What is the slope of this line? c. At what rate does the factory's cost increase for every additional chair produced?
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Linear Functions and Models
The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day. (a) Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the graph. (b) What is the slope of the graph and what does it represent? (c) What is the y-intercept of the graph and what does it represent?
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