5 Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) 0.1x - 1.6x + 6.504, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? The shop should build bicycles.

5 Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) 0.1x - 1.6x + 6.504, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? The shop should build bicycles.

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Description: I put an example of how they want it to be solved from the program. Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) = 0.1x2 - 1.6x + 6.504, where C(x) is in hundreds of dollar

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I put an example of how they want it to be solved from the program.

Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) = 0.1x2 - 1.6x + 6.504, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
The shop should build bicycles.

Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is
given by C(x) = 0.2x2 – 2.3x + 10.357, where C(x) is in hundreds of dollars. How many bicycles should the shop
build to minimize the average cost per bicycle?
The function C(x) gives the average cost per bicycle when x hundred bicycles are made. Notice that this is a
quadratic function where the coefficient of x2 is positive. Therefore, the minimum value will occur at the vertex.
b
Find the x-coordinate of the vertex.
2a
Recall that the x-coordinate of the vertex of a parabola is
b
(- 2.3)
2a
2(0.2)
= 5.75
Remember that x represents bicycles, in hundreds. Determine how many bicycles are represented by x = 5.75.
5.75 • 100 = 575 bicycles
Thus, the shop should build 575 bicycles to minimize the average cost per bicycle.

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