# Case Problem "Julia's Food Booth"

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Assignment #3: Case Problem "Julia's Food Booth"
Mat540
Quantitative Methods
August 22, 2012

Julia’s Food Booth

(A) Formulate and solve a L.P. model for this case. Variables:
Pizza - X1 \$1.33 \$1.50 14 inches
Hot Dogs - X2 \$0.45 \$1.50 16 square inches
Barbecue - X3 \$0.90 \$2.25 25 square inches
Maximize Z= \$0.75x1, 1.05x2, 1.35x3 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: x1 = 1,250 pizza slices x2= 1,250 hot dogs x3= 0 barbecue sandwiches Z= \$2,250 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 |
B) Evaluate the prospect of borrowing money before the first game.
Yes, Julia would increase her profit if she borrowed money from a friend before the first game to purchase more ingredients. Her outcome would be an increase in profit. 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 simply means that Julia can only borrow \$158.88 from her friend, giving her an additional profit of \$238.32.

C) Evaluate the prospect of paying a friend \$100/game to assist.
I believe Julia should hire her friend for \$100 per game. Julia needs the additional help in order to prepare the hot dogs and barbeque sandwiches needed in a short period of time to make her profit. Also, when borrowing the extra \$158.88 from her friend, Julia will be able to pay her friend for the time spent per game for helping with the food booth based on her profit.

D) Analyze the

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