Question

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

(a) The manufacturer can make 2255 bicycles. (b) There are 305 wheels, 50 frames, and 0 handlebars left over. (c) Handlebars limit the production of bicycles.

Step-by-step solution

Calculate the number of bicycles that can be manufactured

To find the number of bicycles that can be manufactured, we will find the minimum value of the following: Bicycles using wheels: \( \dfrac{4815}{2} = 2407.5 \) (but we need a whole number) Bicycles using frames: \( \dfrac{2305}{1} = 2305 \) Bicycles using handlebars: \( \dfrac{2255}{1} = 2255 \) By comparing the three values, we can see the minimum value is 2255. So, the manufacturer can make 2255 bicycles.

Find the leftover parts

To find the leftover parts, we will subtract the used parts from the available parts. Leftover wheels: Wheels – (Bicycles * 2) = 4815 – (2255 * 2) = 4815 – 4510 = 305 wheels left over Leftover frames: Frames – Bicycles = 2305 – 2255 = 50 frames left over Leftover handlebars: Handlebars – Bicycles = 2255 – 2255 = 0 handlebars left over

Identify the limiting part

Since the minimum value for the number of bicycles was found using the handlebars, the handlebars are the part that limits the production of bicycles. In this case, all available handlebars would be utilized in the manufacture of 2255 bicycles with no handlebars left over. So the answers are: (a) 2255 bicycles can be manufactured. (b) 305 wheels, 50 frames, and 0 handlebars are left over. (c) Handlebars limit the production of bicycles.