Julia may lease a warming oven for $600 for a six game football home-season game. the oven has 16 shelves, and each shelf is 3 feet by 4 feet. she plans to fill the oven with the food times (pizza, hot dogs and barbecue sandwiches) before the game and at half time. She has to pay $1,000 per game ($6,000 total) for a booth.
Julia has negotiated with a local pizza delivery coompany to deliver 14 inch cheese pizzas twice each game - two hours before the game and right after the opening kick-off. Each pizza will cost her $6 and will include 8 slices.
She estimates it will cost her $0.45 for each hot dog and $0.90 for each barbecue sandwich if shemakes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 square inches of space and the barbecue sandwich takes up about 25 square inches.
she plans to sell a slice of pizza and a hot dog for $1.50 each
A barbecue sandwich will cost $2.25
She has $1,500 in cash available to purchase and prepare the food itmes for the first home game; for the remaining five games she will purchase the ingredients with money she has made from the previous game.
A. Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth.
B. If Julia were to borrow some more money from a friend before the first game to purchase more ingredients, could she increase her profits? IF so, how much should she borrow and how much additional profit would she make? What factor constrains her from borrowing even more moeny than this amount (indicated in your anser to the previous question?)
C. When Julia looked at the solution in (A), she realized that it would be physically difficult for her to prepare all the hot dogs and barbecue sandwiches in this solution. She believes she can hire a friend of hers to help her for $100 per game. Based on the results in (A) and (B), is this something you think she could reasonably do and should she do it? Why?
D. Julia seems to be basing her analysis on the assumption that everything will go as she plans. What are some of the uncertain factors in the model that could go wrong and adversely affect Julia's analysis?
Given these uncertainties, and the results in (A) and (B) and (C) what do you recommend Julia do?