the calculus of optimization, Managerial Economics

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the demand for widgets(x) is given by:
px=160 -4x
the production of widget has the following average variable cost:
Avc=2x-20
fixed cost are 162
calculate the output level of widget that
a) maximizes total revenue
b) minimizes the average total cost(atc) of widgets
c) minimizes the total cost (tc) of widgets
d)maximizes profits

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