Floor Borders One Foot Wide and of Varying Lengths Are $1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }$

question 11

Short Answer

Floor borders one foot wide and of varying lengths are to be covered with nonoverlapping tiles that are available in two sizes: $1 ^ { \prime } \times 3 ^ { \prime } \text { and } 1 ^ { \prime } \times 5 ^ { \prime }$ sizes. Assuming that the supply of each size is infinite, prove that every $1 ^ { \prime } \times n ^ { \prime }$ border (n > 7) can be covered with these tiles.

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Definitions:

Cost Behavior

The study of how specific costs change in relation to changes in a company's level of activity or volume of output.

Linear

Pertaining to or resembling a line; often used in mathematics to describe a relationship of direct proportionality.

Relevant Range

The range of activity within which the assumptions made about cost behavior are valid.

Variable Costs

Expenses that change in proportion to the amount of goods produced or the volume of sales.