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) The part that limits the production of bicycles is the handlebars.

Step-by-step solution

Determine the required quantity for each part per bicycle

To build a bicycle, you need 2 wheels, 1 frame, and 1 handlebar.

Calculate the number of bicycles that can be made from each part

To find out how many bicycles can be made from each part, divide the total number of each part by the required quantity of that part per bicycle. Wheels: \( \frac{4815}{2} = 2407.5 \) bicycles Frames: \( \frac{2305}{1} = 2305 \) bicycles Handlebars: \( \frac{2255}{1} = 2255 \) bicycles Note: You can't make 0.5 of a bicycle, so the number should be rounded down.

Find the minimum number of bicycles that can be made from all parts

To find the total number of bicycles that can be made, you need to find the minimum number of bicycles that can be made from each part. The smallest number of bicycles that can be made from all parts is 2255 (from handlebars), which is the limiting part. So, the manufacturer can make 2255 bicycles. #b) How many parts of each kind are left over?#

Calculate the number of parts used for making the bicycles

Multiply the limiting number of bicycles (2255) by the required quantity of each part per bicycle. Wheels used: 2255 bicycles * 2 = 4510 wheels Frames used: 2255 bicycles * 1 = 2255 frames Handlebars used: 2255 bicycles * 1 = 2255 handlebars

Calculate the leftover parts

Subtract the number of parts used from the initial quantity. Leftover wheels: 4815 wheels - 4510 wheels = 305 wheels Leftover frames: 2305 frames - 2255 frames = 50 frames Leftover handlebars: 2255 handlebars - 2255 handlebars = 0 handlebars So, there are 305 wheels, 50 frames, and 0 handlebars left over. #c) Which part limits the production of bicycles?#

Identify the limiting part

During the analysis of the problem in part a), we found out that the limiting number of bicycles is 2255, and it was determined by the number of handlebars available. Therefore, the part that limits the production of bicycles is the handlebars.