Mathematics

Restaurant Profits Scenario

You have been placed on a marketing and design team tasked with creating a menu for a swanky new restaurant. Your goal is to design a restaurant menu that will maximize profit.

There are three main roles in this project. Select a role and complete the task listed under the role.

Role #1 Drink Designer
You have 4 drinks to put on the menu: apple, banana, cherry, or dragon fruit. The cost for your restaurant to purchase each bottle of soda is as follows: apple: $4, banana: $3, cherry: $2, dragon fruit: $1. The number of bottles sold every day of each soda depends on the price you set in your menu. The demand for your soda decreases as the price increases.  Here are the formulas for each:
a)    bottles of apple sold = 1.0 x 101 – price
b)    bottles of banana sold = 1.2 x 101 – price
c)    bottles of cherry sold = 1.4 x 101 – price
d)    bottles of dragon fruit = 1.6 x 101 – price
Determine the price of each soda that will give you maximum profit. Include your calculations and results.

Role #2 Main Entree Designer
You have 4 entrees to put on the menu: avocado tacos, burgers, cheese sticks, or deep dish pizza. The cost for your restaurant to make each is the square root of the price you set. The number of entrees sold every day of each depends on the price you set in your menu. The demand for your entrees decrease as the price increases. Here are the formulas for each:
a)    number of avocado tacos sold = 10 x price-2
b)    number of burgers sold = 20 x price-2
c)    number of cheese sticks sold = 30 x price-2
d)    number of deep dish pizzas sold = 40 x price-2
Determine the price of each entree that will give you maximum profit. Include your calculations and results.

Role #3 Dessert Designer
You have 4 desserts to put on the menu: apple pie, baked alaska, cheesecake, or dark chocolate cake. The cost for your restaurant to make each is 60% of the price you set.  The number of desserts sold every day of each depends on the price you set in your menu.  The demand for your desserts decrease as the price increases.  Here are the formulas for each:
a)    number of apple pies sold = 10 – (40% of the price)
b)    number of baked alaskas sold = 15 – (50% of the price)
c)    number of cheesecakes sold = 20 – (60% of the price)
d)    number of dark chocolate cakes sold = 25 – (70% of the price)
Determine the price of each dessert that will give you maximum profit. Include your calculations and results.

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