Question

a farmer sells almonds according to the chart below. the more pounds of almonds that are sold, the lower the cost per pound is for the entire order of almonds.

almond prices

number of pounds	cost (per pound)
more than 10, and up to 20	$15
more than 20, and up to 30	$10
more than 30	$5

the farmer graphs a step function to model the situation, where y represents the cost per pound for an order of x pounds of almonds. which of the following describes the farmer’s graph for the step that includes 20.75 pounds, and what is the total cost of 20.75 pounds of almonds?

• a horizontal segment with an open circle at (20, 10) and a closed circle at (30, 10); $207.50
• a horizontal segment with a closed circle at (20, 10) and an open circle at (30, 10); $207.50
• a horizontal segment with an open circle at (21, 10) and a closed circle at (30, 10); $311.25
• a horizontal segment with a closed circle at (21, 10) and an open circle at (30, 10); $311.25

Explanation:

Step1: Determine the price per pound for 20.75 pounds

From the table, for "more than 20, and up to 30" pounds, the cost per pound is $10. So the step function for this interval will have \( y = 10 \) when \( 20 < x \leq 30 \). In terms of the graph, at \( x = 20 \), since \( x \) must be more than 20, there is an open circle at \( (20, 10) \), and at \( x = 30 \), since \( x \) can be up to 30, there is a closed circle at \( (30, 10) \).

Step2: Calculate the total cost for 20.75 pounds

The formula for total cost is \( \text{Total Cost} = \text{Number of Pounds} \times \text{Cost per Pound} \). Given \( x = 20.75 \) pounds and cost per pound \( = 10 \) dollars. So, \( \text{Total Cost} = 20.75 \times 10 = 207.50 \) dollars.

Answer:

a horizontal segment with an open circle at (20, 10) and a closed circle at (30, 10); $207.50