After formulating and solving a linear programming model for Julia’s Food Booth, I feel that Julia should lease the food booth at the Tech stadium football games. Yes. Julia should lease the booth because she would potentially make a profit of $1150 ($2250-$1100) each game; this is more than what she needs to run the booth. In addition, because she has cash on hand of $1500 to purchase and prepare the food items for the first game, Julia would not have to use any of the money that she makes to buy ingredients for the next game. She could still use the cash that she has on hand to buy ingredients for the next game. Next, if Julia were to borrow some more money from a friend before the first game to purchase more ingredients, she could increase her profit. Julia should borrow $138.40, so that she can make an additional profit of $207.60. An allowable increase in the ‘budget’ constrains her from borrowing more money than this. Because the shadow price for the budget constraint is 1.50 and the allowable increase is 138.40, the budget can go up to 1638.40 and the profit would increase by 1.50 for every dollar that is added to the budget.
Also, Julia should hire a friend of hers to help her for $100 per game. It would be physically difficult and probably too much for her to prepare all of the hot dogs and BBQs before the game and during half time. If she borrows the extra $138.40, she can use a portion of this money to pay her friend without losing out on any money. Lastly, although Julia is basing her analysis on the assumption that everything will go as she plans, there are uncertain factors in the model that could go wrong and adversely affect Julia’s analysis. Some of the uncertain factors in the model are weather and whether or not the people attending the game like or will want to eat pizza, hot dogs and BBQs. The weather may be clear one game and raining another game. There will probably not be as many people attend- ing the game if it is raining or if the weather is not clear. The same thing could happen if it is too hot or too cold. Likewise, there may be some people attending the game that do not like to eat pizza, hot dogs and BBQs or who would rather have a sit-down meal somewhere after the game. Because Julia needs to make, at least, $1100 to pay for the leases of the booth and the oven, she should consider not serving BBQs since they are not benefiting her and not hiring her friend on days when the weather is supposed to be bad. This way, she doesn’t have to pay for the ingredients for the BBQs or pay her friend when there’s not favorable attendance at the game. These cutbacks would probably still cause her to be able to pay for the leases.