Assignment 2
The three products/variables in this problem that must be considered for purchase are: x1: Pizza Slices x2: Hot Dogs x3: Barbeque Sandwiches
The objective is for Julia to maximize profits. Julia’s goal is to earn a profit of at least $1,000.00 after each game.
Profit = Sell – Cost
Profit Function: Z = 0.75(X1) + 1.05(X2) + 1.35(X3)
Constraints and Cost:
The maximum amount of funds available for purchase is $1500.00
Cost per pizza slice = $0.75 because Julia purchases each pizza for $6.00 and there are 8 slices per pizza.
Cost per hot dog = $0.45
Cost per sandwich = $0.90
LPP Model:
Maximize Profit: Z= $0.75x1 + $0.45x2 + $0.90x3 < $1,500
Subject to 24x1 + 16x2 + 25x3 < 55,296 oven space x1 > x2 + x3 (changed to –x1 + x2 + x3 < 0 for constraint) x2/x3 > 2 (changed to –x2 + 2x3 < 0 for constraint) x1, x2, x3 > 0
Solve the LPM:
Pizza(X1) = 1,250; Hotdogs(X2) = 1,250 and Barbecue sandwiches(X3) = 0
Maximum value of Z = $2,250
It would be in Julia’s best interest to stock 1,250 slices of pizza, 1, 250 hot dogs and no barbecue sandwiches as it will yield the maximum profit of $2,250.00 (B) Evaluate the prospect of borrowing money before the first game. I do assert that Julia should borrow money from her friend to increase her profits. The shadow price is $1.50 for each additional dollar Julia earns. The upper limit in the model that is given is $1,658.88. This means that Julia can borrow $158.88 from her friend, which will help her yield an extra profit of $238.32.
(C) Evaluate the prospect of paying a friend $100/game to assist. From the information presented I do believe that Julia should hire her friend to assist her for $100.00 per game. If Julia hires her friend she will receive additional help which will allow her to prepare the food needed within the allotted timeframe to reach her goal. Also essentially Julia is borrowing extra money from another friend, so she has the resources to pay for her friend for time spent helping at the
The objective is for Julia to maximize profits. Julia’s goal is to earn a profit of at least $1,000.00 after each game.
Profit = Sell – Cost
Profit Function: Z = 0.75(X1) + 1.05(X2) + 1.35(X3)
Constraints and Cost:
The maximum amount of funds available for purchase is $1500.00
Cost per pizza slice = $0.75 because Julia purchases each pizza for $6.00 and there are 8 slices per pizza.
Cost per hot dog = $0.45
Cost per sandwich = $0.90
LPP Model:
Maximize Profit: Z= $0.75x1 + $0.45x2 + $0.90x3 < $1,500
Subject to 24x1 + 16x2 + 25x3 < 55,296 oven space x1 > x2 + x3 (changed to –x1 + x2 + x3 < 0 for constraint) x2/x3 > 2 (changed to –x2 + 2x3 < 0 for constraint) x1, x2, x3 > 0
Solve the LPM:
Pizza(X1) = 1,250; Hotdogs(X2) = 1,250 and Barbecue sandwiches(X3) = 0
Maximum value of Z = $2,250
It would be in Julia’s best interest to stock 1,250 slices of pizza, 1, 250 hot dogs and no barbecue sandwiches as it will yield the maximum profit of $2,250.00 (B) Evaluate the prospect of borrowing money before the first game. I do assert that Julia should borrow money from her friend to increase her profits. The shadow price is $1.50 for each additional dollar Julia earns. The upper limit in the model that is given is $1,658.88. This means that Julia can borrow $158.88 from her friend, which will help her yield an extra profit of $238.32.
(C) Evaluate the prospect of paying a friend $100/game to assist. From the information presented I do believe that Julia should hire her friend to assist her for $100.00 per game. If Julia hires her friend she will receive additional help which will allow her to prepare the food needed within the allotted timeframe to reach her goal. Also essentially Julia is borrowing extra money from another friend, so she has the resources to pay for her friend for time spent helping at the