POM Assignment 1:
Problem 1:
The General Store at State University is an auxiliary bookstore located near the dormitories that sells academic supplies, toiletries, sweatshirts and T-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks. The manager of the store has noticed that several pizza delivery services near campus make frequent deliveries. The manager is therefore considering selling pizza at the store. She could buy premade frozen pizzas and heat them in an oven. The cost of the oven and freezer would be $27,000. The frozen pizzas cost $3.75 each to buy from a distributor and to prepare (including labor and a box). To be competitive with the local delivery services, the manager believes she should sell the pizzas for $8.95 apiece. The manager needs to write up a proposal for the university's director of auxiliary services.
a. Determine how many pizzas would have to be sold to break even.
b. If The General Store sells 20 pizzas per day, how many days would it take to break even?
c. The manager of the store anticipates that once the local pizza delivery services start losing business, they will react by cutting prices. If after a month (30 days) the manager has to lower the price of a pizza to $7.95 to keep demand at 20 pizzas per day, as she expects, what will the new break-even point be, and how long will it take the store to break even?
Problem 2:
The Weemow Lawn Service wants to start doing snow removal in the winter when there are no lawns to maintain. Jeff and Julie Weems, who own the service, are trying to determine how much equipment they need to purchase, based on the various job types they have. They plan to work themselves and hire some local college students on a per-job basis. Based on historical weather data, they estimate that there will be six major snowfalls next winter. Virtually all customers want their snow removed no more than 2 days after the snow stops falling. Working 10 hours per day (into the night), Jeff and Julie can remove the snow from a normal driveway in about 1 hour, and it takes about 4 hours to remove the snow from a business parking lot and sidewalk. The variable cost (mainly for labor and gas) per job is $12 for a driveway and $47 for a parking lot. Using their lawn service customer base as a guideline, they believe they will have demand of no more than 40 homeowners and 25 businesses. They plan to charge $35 for a home driveway and $120 for a business parking lot, which is slightly less than the going rate. They want to know how many jobs of each type will maximize their profit.
a. Formulate a linear programming model for this problem.
b. Solve this model graphically.
c. If Jeff and Julie pay $3,700 for snow removal equipment, will they make any money?
d. If Jeff and Julie reduce their prices to $30 for a driveway and $100 for a parking lot, they will increase demand to 55 for driveways and 32 for businesses. Will this affect their possible profit?
e. Alternatively, hiring additional people on a per-job basis will increase Jeff and Julie's variable cost to $16 for a driveway and $53 for a parking lot, but it will lower the time it takes to clear a driveway to 40 minutes and a parking lot to 3 hours. Will this affect their profit?
f. If Jeff and Julie combine the two alternatives suggested in (d) and (e), will this affect their profit?