You Have Supplies of Boards That Are One Foot, fiVe

question 42

Essay

You have supplies of boards that are one foot, five feet, seven feet, and twelve feet long. You need to lay pieces end-to-end to make a molding 15 feet long and wish to do this using the fewest number of pieces possible. Explain why the greedy algorithm of taking boards of the longest length at each stage (so long as the total length of the boards selected does not exceed 15 feet) does not give the fewest number of boards possible.

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Definitions:

Short-Run Supply Curve

A graphical representation showing the quantity of goods that producers are willing to supply at different prices in the short term, when at least one input is fixed.

Business Owner

An individual or entity that possesses and oversees the operations of a company or enterprise, ensuring its functionality and aiming for its success.

Profitability

The degree to which a business or activity yields profit or financial gain, measured by the ratio of profit to revenues or investment.