48. Consider the following break-even problem: the cost of producing Q units, c(Q), is described by the curve c(Q) = 48Q[1 – exp(-.08Q)], where Q is in hundreds of units of items produced and c(Q) is in thousands of dollars. a. Graph the function c(Q). What is its shape? What economic phenomenon gives rise to a cumulative cost curve of this shape? b. At what production level does the cumulative production cost equal $1,000,000? c. Suppose that these units can be purchased from an outside supplier at a cost of $800 each, but the firm must invest $850,000 to build a facility that would be able to produce these units at a cost c(Q). At what cumulative volume of production does it make sense to invest in the facility?
48. Consider the following break-even problem: the cost of producing Q units, c(Q), is described by the curve c(Q) = 48Q[1 – exp(-.08Q)], where Q is in hundreds of units of items produced and c(Q) is in thousands of dollars. a. Graph the function c(Q). What is its shape? What economic phenomenon gives rise to a cumulative cost curve of this shape? b. At what production level does the cumulative production cost equal $1,000,000? c. Suppose that these units can be purchased from an outside supplier at a cost of $800 each, but the firm must invest $850,000 to build a facility that would be able to produce these units at a cost c(Q). At what cumulative volume of production does it make sense to invest in the facility?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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![48. Consider the following break-even problem: the cost of producing Q units, c(Q), is
described by the curve
c(Q) = 48Q[1 – exp(-.08Q)],
where Q is in hundreds of units of items produced and c(Q) is in thousands of
dollars.
a. Graph the function c(Q). What is its shape? What economic phenomenon gives rise
to a cumulative cost curve of this shape?
b. At what production level does the cumulative production cost equal
$1,000,000?
c. Suppose that these units can be purchased from an outside supplier at a cost of $800
each, but the firm must invest $850,000 to build a facility that would be able to
produce these units at a cost c(Q). At what cumulative volume of production does
it make sense to invest in the facility?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe59ce603-79e4-4e95-9ec4-a5a97c04e980%2F3f9f75ee-e419-4d7f-8ca4-bce79482d6ae%2Ff5xehvk.png&w=3840&q=75)
Transcribed Image Text:48. Consider the following break-even problem: the cost of producing Q units, c(Q), is
described by the curve
c(Q) = 48Q[1 – exp(-.08Q)],
where Q is in hundreds of units of items produced and c(Q) is in thousands of
dollars.
a. Graph the function c(Q). What is its shape? What economic phenomenon gives rise
to a cumulative cost curve of this shape?
b. At what production level does the cumulative production cost equal
$1,000,000?
c. Suppose that these units can be purchased from an outside supplier at a cost of $800
each, but the firm must invest $850,000 to build a facility that would be able to
produce these units at a cost c(Q). At what cumulative volume of production does
it make sense to invest in the facility?
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a) Determine the shape of the graph of function c(Q):
VIEWFormulae to compute the table in above step:
VIEWb) Determine the production level when the cumulative production cost is $1,000,000:
VIEWc) Determine the cumulative volume of production that make sense to invest in the facility:
VIEWFormulae to compute the table:
VIEW
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