# Assignment # 3 Math 540

Pages: 2 (467 words) Published: September 16, 2012
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...