Case Problem "Julia's Food Booth"
Running Head: JULIA’S FOOD BOOTH
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
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