a craft vendor must sell at least $300 worth of merchandise to make a profit. scarves sell for $10 each and…

a craft vendor must sell at least $300 worth of merchandise to make a profit. scarves sell for $10 each and hats sell for $20 each. she expects to sell at least 20 items. the lines on the graph represent the situation in which she makes a profit. in which section of the graph does the actual solution lie? 1 2 3 4

a craft vendor must sell at least $300 worth of merchandise to make a profit. scarves sell for $10 each and hats sell for $20 each. she expects to sell at least 20 items. the lines on the graph represent the situation in which she makes a profit. in which section of the graph does the actual solution lie? 1 2 3 4

Answer

Explanation:

Step1: Set up inequalities

Let $x$ be the number of scarves sold and $y$ be the number of hats sold. The profit - making condition is $10x + 20y\geq300$ (simplifies to $x + 2y\geq30$), and the number - of - items condition is $x + y\geq20$.

Step2: Analyze the regions

Region 1: Points in this region satisfy both $x + 2y\geq30$ and $x + y\geq20$. Region 2: Points here do not satisfy $x + 2y\geq30$. Region 3: Points here do not satisfy $x + y\geq20$. Region 4: Points here do not satisfy either $x + 2y\geq30$ or $x + y\geq20$.

Answer:

1