SOLUTION: Exercise 275 It costs a business $11,300 to manufacture 20 golden widgets. It costs the same business $17,750 to manufacture 50 golden widgets. In a coordinate plane sketch the lin
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Question 627743: Exercise 275 It costs a business $11,300 to manufacture 20 golden widgets. It costs the same business $17,750 to manufacture 50 golden widgets. In a coordinate plane sketch the line that passes through the given points where the number of golden widgets x is the horizontal axis and the cost $C to manufacture the golden widgets is the vertical axis.
(a) The slope of the line that passes through the given points gives the cost of production per golden widget, called the marginal cost. Find the marginal cost of the golden widgets.
(b) The vertical-intercept of the line that passes through the given points gives the fixed cost of manufacturing golden widgets. Find the fixed cost of manufacturing the golden widgets.
(c) Using the slope-intercept form, find an equation of the line that gives the cost $C of manufacturing x golden widgets.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Plot the points )
and )
on your coordinate axes and then sketch a line that passes through the two points. Unless you have some really, really tall paper, you will want to scale your coordinate plane appropriately, say units of 1000 on the vertical axis against units of 5 on the horizontal.
Start with part (c). First use the two-point form of an equation of a line:
(x\ -\ x_1) )
where )
and )
are the coordinates of the given points.
Plug in the numbers, do the arithmetic, simplify, and solve for 
in terms of everything else. Once your equation has the form:
you have completed part (c).
The answer to part (a) is the coefficient on 
in your answer to (c).
The answer to part (b) is the constant term, i.e., the 
in your answer to part (c).
John
My calculator said it, I believe it, that settles it
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