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Chapter 3: Problem 69

A manufacturer of bicycles has 4815 wheels, 2305 frames, and 2255 handlebars. (a) How many bicycles can be manufactured using these parts? (b) How many parts of each kind are left over? (c) Which part limits the production of bicycles?

Short Answer

Expert verified
(a) The manufacturer can produce 2255 bicycles using all the available parts. (b) The remaining parts are: 305 wheels, 50 frames, and 0 handlebars. (c) The part that limits the production of bicycles is the handlebars.

Step by step solution

01

Understand the requirements to build a bicycle

To manufacture a complete bicycle, we need the following parts: - 2 wheels - 1 frame - 1 handlebar
02

Calculate how many bicycles can be produced using all the available parts

We'll divide the number of parts by the required amount for each component and then find the minimum number of bicycles that can be produced: Wheels: \( \frac{4815}{2} = 2407.5 \) (round down to 2407 bicycles) Frames: \( \frac{2305}{1} = 2305 \) bicycles Handlebars: \( \frac{2255}{1} = 2255 \) bicycles The minimum number of bicycles that can be produced is 2255 (limited by the number of handlebars).
03

Determine the number of parts left over for each component

Wheels: 4815 - (2 * 2255) = 305 wheels left over Frames: 2305 - 2255 = 50 frames left over Handlebars: 2255 - 2255 = 0 handlebars left over
04

Identify the part that limits the production of bicycles

The component that limits the production of bicycles is the handlebars, with 2255 available.
05

Summary of the solution

(a) The manufacturer can produce 2255 bicycles using all the available parts. (b) The remaining parts are: 305 wheels, 50 frames, and 0 handlebars. (c) The part that limits the production of bicycles is the handlebars.

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