The Possibility Restaurant Essay

919 Words Jul 1st, 2012 4 Pages
“The Possibility” Restaurant Problem
Angela Fox and Zooey Caulfield were food and nutrition majors at State University, as well as close friends and roommates. Upon graduation Angela and Zooey decided to open a French restaurant in Draperton, the small town where the university was located. There were no other French restaurants in Draperton, and the possibility of doing something new and somewhat risky intrigued the two friends. They purchased an old Victorian home just off Main Street for their new restaurant, which they named "The Possibility".

Angela and Zooey knew in advance that at least initially they could not offer a full varied menu of dishes. They had no idea what their local customers' taste in French cuisine would be, so
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Part B2 (where the fish and beef dinner profit are the same):
The Objective Function:
Max Z = 16X1 + 16X2, since the profit of the meals are both the same
Constraints:
X1 + X2 <= 60 (Maximum meal each night)
0.25X1 + 0.50X2 <= 20 (Maximum labor hours allowed each day)
2X1 – 3X2 >= 0 (Ratio 3 Fish Dinners to 2 Beef Dinners)
0.8X2 – 0.2X1 >= 0 (Now, at least 20% of the customers will have the Beef Dinners)
X1, X2 >= 0 (non-negativity constraint)

Point A: Point B: Point C: Point D: Point E:
X1 = 0 X1 = 34 X1 = 40 X1 = 54 X1 = 60
X2 = 40 X2 = 22 X2 = 20 X2 = 6 X2 = 0
Z = $640 Z =$896 Z = $960 Z = $960 Z = $960
Since the objective function has changed and the both dinner retain the same profit the optimal point will be anywhere on the line segment CE. This will give a maximum profit of $960 a day.
To make a maximum profit for Angela and Zooey they will need to increase the price of fish dinners so that both fish and beef dinners earn a profit of $16 each. This will give them a maximum profit of $960.00 per day. When the profits are the same for both dinners then the optimal point will give the maximum profit at any point on the line segment

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