Jim’s fundraiser BBQ needs to make at least $1000 in sales on Saturday. He sells hot dogs for $2 each and hamburgers for $3 each, and he wants to sell at least twice as many hamburgers as hot dogs. He brought 300 hot dogs and 800 hamburgers to sell.
The graph shows the feasible region, where x represents the number of hot dogs sold and y represents the number of hamburgers sold.
Which ordered pairs meet all the constraints for a successful fundraiser and make sense in context of the situation?
Select each correct answer.
To find the ordered pairs that meet all the constraints, we need to consider the following conditions:
1. The total sales must be at least $1000.
2. The number of hamburgers sold must be at least twice the number of hot dogs sold.
Let's analyze each option:
Option 1: (400 hot dogs, 800 hamburgers)
Total sales = (400 * $2) + (800 * $3) = $800 + $2400 = $3200
This option satisfies both conditions.
Option 2: (300 hot dogs, 600 hamburgers)
Total sales = (300 * $2) + (600 * $3) = $600 + $1800 = $2400
This option satisfies both conditions.
Option 3: (500 hot dogs, 1000 hamburgers)
Total sales = (500 * $2) + (1000 * $3) = $1000 + $3000 = $4000
This option satisfies both conditions.
Option 4: (300 hot dogs, 800 hamburgers)
Total sales = (300 * $2) + (800 * $3) = $600 + $2400 = $3000
This option satisfies both conditions.
Therefore, the ordered pairs that meet all the constraints and make sense in the context of the situation are:
Option 1: (400 hot dogs, 800 hamburgers)
Option 2: (300 hot dogs, 600 hamburgers)
Option 3: (500 hot dogs, 1000 hamburgers)
Option 4: (300 hot dogs, 800 hamburgers)