Mat540 Assignment 3
A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations.
Let, X1 =No of pizza slices,
X2 =No of hot dogs,
X3 = No of barbeque sandwiches
* Objective function co-efficient:
The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price.
For Pizza slice, Cost/slice=$4.5/6=$0.75 | X1 | X2 | X3 | SP | $1.50 | $1.60 | $2.25 | -Cost | 0.75 | $0.50 | $1.00 | Profit | $0.75 | $1.10 | $1.25 |
Maximize Total profit Z = $0.75X1 + 1.10X2 +1.25X3
* Constraints:
1. Budget constraint:
0.75X1+0.50X2+1.00X3= 2.0 (at least twice as many hot dogs as barbeque sandwiches)
This constraint can be rewritten as:
X2-2X3>=0
X1, X2, X3 >= 0
Model:
Maximize Total profit Z = $0.75X1 + 1.10X2 +1.25X3
Subject to:
0.75X1+0.50X2+1.00X3=0 (at least twice as many hot dogs as barbeque sandwiches)
X1, X2, X3 >= 0 (Non negativity constraint)
B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.
Do an analysis of the profit solution and what impact it has on Julia’s ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
Target Cell (Max) | | | | | | Cell | Name | Original Value | Final Value | | | | $E$6 | | $ 2,102.01 | $ 2,102.01 | | | | | | | | | | | | | | | | | Adjustable Cells | | | | |
Let, X1 =No of pizza slices,
X2 =No of hot dogs,
X3 = No of barbeque sandwiches
* Objective function co-efficient:
The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price.
For Pizza slice, Cost/slice=$4.5/6=$0.75 | X1 | X2 | X3 | SP | $1.50 | $1.60 | $2.25 | -Cost | 0.75 | $0.50 | $1.00 | Profit | $0.75 | $1.10 | $1.25 |
Maximize Total profit Z = $0.75X1 + 1.10X2 +1.25X3
* Constraints:
1. Budget constraint:
0.75X1+0.50X2+1.00X3= 2.0 (at least twice as many hot dogs as barbeque sandwiches)
This constraint can be rewritten as:
X2-2X3>=0
X1, X2, X3 >= 0
Model:
Maximize Total profit Z = $0.75X1 + 1.10X2 +1.25X3
Subject to:
0.75X1+0.50X2+1.00X3=0 (at least twice as many hot dogs as barbeque sandwiches)
X1, X2, X3 >= 0 (Non negativity constraint)
B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.
Do an analysis of the profit solution and what impact it has on Julia’s ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
Target Cell (Max) | | | | | | Cell | Name | Original Value | Final Value | | | | $E$6 | | $ 2,102.01 | $ 2,102.01 | | | | | | | | | | | | | | | | | Adjustable Cells | | | | |