Manufacturing—Bicycles: For Exercise, the Wheelex Company manufactures bicycles and finds the price function for the bicycles to be
p(x) = −0.02x + 190
where x represents the number of bicycles produced and sold and p(x) is the price of the bicycle. Furthermore, the fixed and variable costs to produce x bicycles are $5600 and $85 per bicycle, respectively.
Using the information found in Exercise 1, complete parts (a) through (d).
(a) Evaluate MC(250) and MC(500) and interpret these answers.
(b) Why are the answers in part (a) equal?
(c) Algebraically find AC(x) and simplify.
(d) Evaluate AC(250) and interpret.
Exercise 1
Manufacturing—Bicycles: For Exercise 1, the Wheelex Company manufactures bicycles and finds the price function for the bicycles to be
p(x) = −0.02x + 190
where x represents the number of bicycles produced and sold and p(x) is the price of the bicycle. Furthermore, the fixed and variable costs to produce x bicycles are $5600 and $85 per bicycle, respectively.
The cost function follows the linear form C(x) = mx + b. Answer the following.
(a) Write the cost C in the linear form C(x) = mx + b.
(b) Use calculus to compute the marginal cost function.
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