Julia’s Food Booth
A.Formulate and solve an L.P. model for this case.
Decision Variables |
X1 | # of Pizzas |
X2 | # of Hotdogs |
X3 | # of BBQ Sandwiches |
Objective Function |
| X1 | X2 | X3 |
Selling Price | $ 1.50 | $ 1.50 | $ 2.25 |
Cost | $ 0.75 | $ 0.45 | $ 0.90 |
Profit | $ 0.75 | $ 1.05 | $ 1.35 |
Maximize total profit Z=$0.75X1+$1.05X2+$1.35X3
Budget Constraints: $0.75X1+$0.45X2+$0.90X3<=$1,500
Space Constraints: 3x4x16= 196 Sq. Ft., 192x12x12=27,648 In Sq.
Oven will be filled at the beginning and halftime of the game: 2x27, 648=55,296 In. Sq.
Space for Pizza: 14x14=196 In. Sq., 196/8(Slices) =24.5 In. ...view middle of the document...
The objective function on the first page demonstrates the selling price, cost, and profit for each food item. The constraints were based on the budget Julia had and the space in her oven for the food. Also there is the information of how much pizza, hotdogs, and BBQ sandwiches she would sell compared to each other. To solve the linear program the objective function and the constraints had to be used together. The results from the program show that if Julia sells 1,250 slices of pizza and 1,250 hotdogs she would have a profit of $2,250.
If Julia goes with this linear solution she will not need to invest in the BBQ sandwiches. As illustrated above Julia needs to sell 1,250 pizza slices and the same amount of hotdogs to make a profit. Her expense for one game is $1,000 for the booth and $100 for the oven for a total of $1,100. The linear program’s solution demonstrates that she will make $2,250 for one game. Therefore the total expenses (1,100) can be subtracted from the revenue she will make for the first game (2,250). In turn she will clear $1,150 after expenses and that is $150 over what she wanted to at least make to consider the venture a success.
B.Evaluate the prospect of borrowing money before the first game.
Borrowing money before the first game is an option that Julia could consider. Based on the linear program that was explained in the beginning of this paper it does not make sense to borrow money for the first game. As the linear program has shown Julia has enough money to purchase the food she needs to turn a profit that can pay for the booth, oven rental, and for her to make an income. Borrowing money before the first game only adds to the constraints in the program. Julia would have to consider the constraint of having to make payments, pay interest on the borrowed money, and borrowing the money when she really does not need it.
If Julia did not have the funds to pay for the food to sell or to rent the booth and the oven she would need to borrow money before the first game. After the first game she may make enough money where she could pay off her loan and use her own money to keep going. But since she does have the money to start the business it is better to use it then to borrow. Borrowing gets other people involved and would put additional pressure onto Julia.
C.Evaluate the prospect of paying a friend $100/game to assist.
To evaluate the prospect of hiring a friend to help out Julia would need to weigh the benefits to such an idea. The solution to the linear program has shown that Julia will clear $1,150 for one game. If she were to hire a friend to help she would have to add the $100 she is paying the...