Assignment # 3 Math 540
Assignment #3: Case Problem "Julia's Food Booth" Page 1
Case Problem "Julia's Food Booth"
Jenna Kiragis
Strayer University
8/24/2012
Assignment #3: Case Problem "Julia's Food Booth" Page 2
A) Formulate and solve an L.P. model:
Variables:
x1 – Pizza Slices x2 – Hot Dogs x3 – Barbeque Sandwiches
Subject to:
$0.75x1 + $0.45x2 + $0.90x3 ? $1,500
24x1 + 16x2 + 25x3 ? 55,296 in2 of 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
Solution:
Variable | Status | Value |
X1 | Basic | 1250 |
X2 | Basic | 1250 |
X3 | NONBasic | 0 | slack 1 | NONBasic | 0 | slack 2 | Basic | 5296.0 | slack 3 | NONBasic | 0 | slack 4 | Basic | 1250 |
Optimal Value (Z) | | 2250 |
Assignment #3: Case Problem "Julia's Food Booth" Page 3
B) Evaluate the prospect of borrowing money before the first game.
Yes, Julia would increase her profit if she borrowed some more money from a friend. The shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can only borrow $158.88 from her friend, giving her an additional profit of $238.32. Based on the sensitivity analysis, the upper limit of the sensitivity range for budget is $158.00 allowing her to have a maximum budget of $1658.00. Her shadow price reflects an increase of $1.50 for any additional resource. Therefore if she borrows the maximum of $158.88, she will yield an increase in profit of $238.32 and total profit of $2,488.32.
C) Prospect of paying a friend $100/game to assist
Yes, I believe Julia should hire her friend for $100 per game. In order for Julia to prepare the hot dogs and barbeque sandwiches needed in a short period of time to make her profit, she needs the additional help. Also, with
Case Problem "Julia's Food Booth"
Jenna Kiragis
Strayer University
8/24/2012
Assignment #3: Case Problem "Julia's Food Booth" Page 2
A) Formulate and solve an L.P. model:
Variables:
x1 – Pizza Slices x2 – Hot Dogs x3 – Barbeque Sandwiches
Subject to:
$0.75x1 + $0.45x2 + $0.90x3 ? $1,500
24x1 + 16x2 + 25x3 ? 55,296 in2 of 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
Solution:
Variable | Status | Value |
X1 | Basic | 1250 |
X2 | Basic | 1250 |
X3 | NONBasic | 0 | slack 1 | NONBasic | 0 | slack 2 | Basic | 5296.0 | slack 3 | NONBasic | 0 | slack 4 | Basic | 1250 |
Optimal Value (Z) | | 2250 |
Assignment #3: Case Problem "Julia's Food Booth" Page 3
B) Evaluate the prospect of borrowing money before the first game.
Yes, Julia would increase her profit if she borrowed some more money from a friend. The shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can only borrow $158.88 from her friend, giving her an additional profit of $238.32. Based on the sensitivity analysis, the upper limit of the sensitivity range for budget is $158.00 allowing her to have a maximum budget of $1658.00. Her shadow price reflects an increase of $1.50 for any additional resource. Therefore if she borrows the maximum of $158.88, she will yield an increase in profit of $238.32 and total profit of $2,488.32.
C) Prospect of paying a friend $100/game to assist
Yes, I believe Julia should hire her friend for $100 per game. In order for Julia to prepare the hot dogs and barbeque sandwiches needed in a short period of time to make her profit, she needs the additional help. Also, with