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Profit with Varying Price The background for this exercise can be found in Exercises 15, 16, 17, and 18 in Section 1.4. A manufacturer of widgets has fixed costs of $1200 per month, and the variable cost is $40 per widget (so it costs $40 to produce 1 widget). Let N be the number of widgets product in a month.
a. Find a formula for the manufacturer’s total cost C as a function of N.
b. The highest price P, in dollars, of a widget at which N widgets can be sold is given by the formula
c. Use your answers to parts a and b to find a formula for the profit P of this manufacturer as a function of N.
d. Use your formula for part c to determine the two break-even points for this manufacturer. Assume here that the manufacturer produces the widgets in blocks of 50, so a table setup showing N in multiples of 50 is appropriate.
e. Use your formula from part c to determine the production level at which product is maximized if the manufacturer can produce at most 1500 widgets in a month. As in part d, assume that the manufacturer produces the widgets in blocks of 50.
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