1
Mexican fast food

• Greg Gerold
• Harry Wong
• ESE 251

2
Model

• Open 70 hours a week
• Taxes/ Rent -gt 2000 USD per week
• Labor Cost -gt 10 USD/hr
• Weighted average cost of all items -gt 2.53
  USD/item

3
Regimes

• WAP (weighted average price) of 6.50 USD
• 40 items were sold per an hour and 6 people were
  required
• WAP of 7 USD
• 20 items were sold per an hour and 4 people were
  needed

4
Profit

• Profit total revenue total cost
• _at_ 6.50 4,916
• _at_ 7.00 1,463
• Is there a price regime within the range that
  maximizes profit?

5
Model

• Cobb - Douglas Equation
• Based on least squares regression fitting of
  statistical data.
• are constants with respect to time.
• Beta 1 as K is constant
• L man hours
• K capital (rent, taxes)
• Y productivity factor

6
Solutions

• Algebraic solution
• Two regimes two unknowns
• Y 0.0000484
• alpha1.71

7
Optimization

• Profit Total Revenue Total Cost
• Optimal at
• 0 Marginal revenue Marginal Cost

8
Marginal Functions
9
Demand Estimation

• Assume demand can be modeled by
• P(Q) a bQ
• 7.00a - b 1400
• 6.50a b 2800
• Solve two simultaneous linear equations
• a 7.49, b0.000357

10
Finding the Optimal Solution

• There are two solutions within the domain
• One is 2 burritos a week
• The other is 11,120 burritos
• So plugging in this quantity to the Profit
  equation we get
• 6574/week

11
Logistics

• Labour
• 13.5 employees working 70 hour weeks
• 944 total hours
• Pricing
• 3.97

12
Analysis

• Sensitivity
• Price
• Quantity
• What if?