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October 9th, 2009, 08:41 AM   #1
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No one can seem to answer this?

The question:

The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.

The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced.

The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then the manufacturer is at a break-even point.

A manufacturer of widgets has fixed costs of $1725 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 produced in a month.

(a) Use the formula 53N-(40N+1725) 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.

____widgets/mo (smaller value)
____widgets/mo (larger value)

(b) Use the formula 53N-(40N+1725) to determine the production level at which profit is maximized if the manufacturer can produce at most 1500 widgets in a month. As in part (a), assume that the manufacturer produces the widgets in blocks of 50.

____


Okay... no one seems to be able to answer this problem. I am completely and utterly stuck... the book isn't helping much, either.
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October 9th, 2009, 10:53 AM   #2
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Re: No one can seem to answer this?

a) Use 13N - 1725 = 0. What do you get for N? Remember that widgets are produced in blocks of 50.

b) Given that N may not exceed 1500, the profit function P(N) = 13N - 1725 is at a maximum when N = 1500, which is a multiple of 50.
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