24. When a wind generator is installed there is a substantial initial cost, but daily operation requires no further cash payment. However, to keep the generator in proper operating con- dition, it must undergo maintenance once a year. Each maintenance cycle requires a cash payment of $5000. The solid lines on the following graph show this situation. The stepped blue line shows the cost over time and the straight brown line shows the revenue derived from the generator. As the second yearly maintenance approaches, you are informed by the manufacturer that a significant upgrade is available for additional cost. The upgrade will make the genera- tor far more efficient, thus the revenue would increase substantially. The yearly maintenance cost after the upgrade would still be $5000. The dashed lines show the cost and revenue projections if the upgrade is installed. (a) What is the amount of revenue per year without the upgrade? (b) What is the initial cost of the wind generator? (c) How many years after the initial installation do you break even if the upgrade is installed? List your answer as number of years + number of months. (d) What is the cost of the upgrade completed at the two-year maintenance cycle? Note that this amount includes the standard $5000 maintenance fee.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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24. When a wind generator is installed there is a substantial initial cost, but daily operation
requires no further cash payment. However, to keep the generator in proper operating con-
dition, it must undergo maintenance once a year. Each maintenance cycle requires a cash
payment of $5000. The solid lines on the following graph show this situation. The stepped
blue line shows the cost over time and the straight brown line shows the revenue derived
from the generator.
As the second yearly maintenance approaches, you are informed by the manufacturer
that a significant upgrade is available for additional cost. The upgrade will make the genera-
tor far more efficient, thus the revenue would increase substantially. The yearly maintenance
cost after the upgrade would still be $5000. The dashed lines show the cost and revenue
projections if the upgrade is installed.
(a) What is the amount of revenue per year without the upgrade?
(b) What is the initial cost of the wind generator?
(c) How many years after the initial installation do you break even if the upgrade is
installed? List your answer as number of years + number of months.
(d) What is the cost of the upgrade completed at the two-year maintenance cycle? Note
that this amount includes the standard $5000 maintenance fee.

100,000
Breakeven Analysis for Wind Generator
Cost without upgrade
80,000
Revenue without upgrade
Cost with upgrade
Revenue with upgrade
60,000
40,000
20,000
al obor
3
6.
0.
om bo
1
Time (t) [yr]
(e) How many years after the initial installation would the profit be the same whether you
upgrade or not? List your answer as number of years + number of months.
(1) How many years after the initial installation will you have made a profit of $25,000 if
the upgrade is NOT installed? List your answer as number of years + number of
months.
(g) If the upgrade results in increased reliability, thus increasing the maintenance interval
to two years, though still at a cost of $5000 per maintenance, how many years after the
initial installation will you break even after the upgrade? List your answer as number
of years + number of months.
Cost (C) and Revenue (R) [$]

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