Question

Jeff and Sargon are saving money to go on a road trip. After looking at all the costs, they determine they need at least $2050 to go on the trip. Jeff shovels snow from driveways and Sargon salts the sidewalks to raise money. Jeff charges $12 each time he shovels a driveway and Sargon charges $8 each time he salts a sidewalk. The number of sidewalks that Sargon has scheduled is no more than four times the number of driveways Jeff has scheduled to shovel. Sargon plans to salt at least 32 sidewalks through the winter season.Write a set of constraints to model the problem, with x representing the number of driveways shoveled and y representing the number of sidewalks salted. You should write a total of 3 constraints.

Answer 1

• 12x + 8y ≥ 2050

,

• y ≤ 4x

,

• y ≥ 32

Step-by-step explanation

First, we have to name the variables:

• x: the number of driveways Jeff shovels

,

• y: the number of sidewalks Sargon salts

We know that Jeff charges $12 for each driveway he shovels and Sargon charges $8 for each sidewalk he salts. This means that for x driveways shoveled and y sidewalks salted, they will earn 12x + 8y. For their road trip, they need at least $2050, so their total earnings must be $2050 or more.

Therefore, the first constraint is 12x + 8y ≥ 2050.

Then, we know that the number of sidewalks Sargon will salt, y, will be no more than four times the number of driveways Jeff will shovel. This means that the second constraint is y ≤ 4x.

Finally, we know that Sargon plans to salt at least 32 sidewalks, which is the same as saying "32 sidewalks or more". Hence, the third constraint is y ≥ 32.