Question

question 3 of 10
norman wants to spend some time drawing and using the computer before
dinner.

dinner will be ready in 45 minutes or less.
he wants to spend at least 25 minutes drawing.

which graph represents the amounts of time norman can spend drawing and
using the computer?

a. graph with drawing time (minutes) on x - axis, computer time (minutes) on y - axis, a red vertical line and a red line with negative slope, blue shaded region
text description for graph

b. graph with drawing time (minutes) on x - axis, computer time (minutes) on y - axis, a red horizontal line and a red line with negative slope, blue shaded region
text description for graph

c. graph with drawing time (minutes) on x - axis, computer time (minutes) on y - axis, a red vertical line and a red line with negative slope, green shaded region
text description for graph

another graph with drawing time (minutes) on x - axis, computer time (minutes) on y - axis, a red line with negative slope
text description for graph

Explanation:

Step1: Define Variables

Let \( x \) be the drawing time (minutes) and \( y \) be the computer time (minutes).

Step2: Set Up Inequalities

1. Total time: \( x + y \leq 45 \) (dinner in 45 min or less).

Rewrite: \( y \leq -x + 45 \) (line with slope -1, y-intercept 45, solid line, shade below).

1. Drawing time: \( x \geq 25 \) (at least 25 min drawing).

This is a vertical line \( x = 25 \), solid line, shade to the right.

Step3: Analyze Graphs

• The inequality \( x \geq 25 \) requires a vertical line at \( x = 25 \) (eliminates options without this, like B).
• The inequality \( y \leq -x + 45 \) is a line with negative slope.
• The feasible region is where \( x \geq 25 \) and \( y \leq -x + 45 \) (shaded region to the right of \( x = 25 \) and below \( y = -x + 45 \)).

Answer:

Assuming the correct graph (e.g., Option A if it matches the vertical line \( x = 25 \) and the line \( y = -x + 45 \) with the shaded region at their intersection), the answer is the graph with \( x \geq 25 \) (vertical line) and \( y \leq -x + 45 \) (negative -sloped line) shaded. For example, if Option A has these features, the answer is:

A. [Graph with vertical line at \( x = 25 \), line \( y = -x + 45 \), and shaded region to the right of \( x = 25 \) and below \( y = -x + 45 \)]