Lee works behind the deli counter at a grocery store. Since he ran out of macaroni salad last night, Lee made 15 pounds, or 240 ounces, of macaroni salad this morning to sell behind the counter. Customers can purchase individual-size containers that hold 6 ounces of macaroni salad or family-size containers that hold 16 ounces. Graph the inequality that represents how many individual-size containers, x, and family-size containers, y, Lee can sell. Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.

Question

Lee works behind the deli counter at a grocery store. Since he ran out of macaroni salad last night, Lee made 15 pounds, or 240 ounces, of macaroni salad this morning to sell behind the counter. Customers can purchase individual-size containers that hold 6 ounces of macaroni salad or family-size containers that hold 16 ounces. Graph the inequality that represents how many individual-size containers, x, and family-size containers, y, Lee can sell. Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.

Answer 1

The inequality that represents how many individual-size containers, x, and family-size containers, y, Lee can sell is:

6x + 16y <= 240

To graph the boundary line and plot points, we can first rewrite the inequality in slope-intercept form:

16y <= -6x + 240
y <= -3/8x + 15

Now we can plot points on the boundary line and graph the inequality. We will shade the region below the line since it represents the feasible region for the number of containers Lee can sell.

(0,15) is a point on the boundary line
(40,0) is another point on the boundary line

Select the solid line below to indicate the boundary line:
solid

Now, shade the region below the boundary line to represent the feasible region:

Select the region below the boundary line to shade it:
below