Question

The Reeves twins are in the yard maintenance business. They want to start doing snow removal during the winter season because they practically don't have any yards to maintain. The twins are trying to determine how much equipment they need to purchase. The twins plan to do most of the work themselves and then hire some part-time workers on an individual job basis to help out.
The twins gathered some data on past weather. Based on the information, they predict that there will be six big snowstorms in the coming winter. Most of their clients want the snow removed no more than two days after the snow stops falling. If the twins work for 10 hours a day, they can remove the snow from the driveway of a home in about 1 hour. However, for commercial parking lots and public sidewalks, it will take 4 hours.

The variable cost per job is $12 for home driveways and $47 for commercial parking lots. The twins estimated that they will have no more than 40 homeowners and 25 businesses who would like to have snow removed. The twins are planning to charge $35 for a home driveway and $120 for commercial parking lots. The twins believe they can get more clients because this is less than the prices their current competitors are charging. The twins would like to know how many jobs of each type will maximize their profit.

Instructions:
Part 1:
Formulate and show your complete linear programming model for this problem.
Type your final answer in the space provided for this problem.

Answer 1

Let the twins remove snow from x home driveways and y commercial parking lots and public sidewalks

Variable cost per job is 12 for home and 47 for commercial

Twins plan to charge 35 for home and 120 for commercial

Hence profit for home will be 35-12 = 23 and commercial will be 120-47 = 73

Hence total profit for the twins = 23x + 73y that needs to be maximized

There will be six big snowstorms in the coming winter and twins work 10 hours a day

Hence total time available = 60 hours

Time required to remove snow from driveway of a home is 1 hr

Time required to remove snow from commercial parking lots and public sidewalks is 4 hrs

Hence x + 4y <= 60 is the time constraint

Futher, there will be no more than 40 homeowners and 25 businesses

hence x <= 40 and y <= 25

Also, x,y >= 0