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Optimizing Mexican Fast Food Profits: A Detailed Analysis

Explore the profitability optimization of a Mexican fast food restaurant with statistical modeling and regression equations. Discover the ideal pricing strategies, labor costs, and productivity factors to maximize profits. Gain insight into demand estimation, finding optimal solutions, and logistics analysis for efficient operations.

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Optimizing Mexican Fast Food Profits: A Detailed Analysis

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  1. “Mexican” fast food Greg Gerold Harry Wong ESE 251

  2. Model • Open 70 hours a week • Taxes/ Rent … -> 2000 USD per week • Labor Cost -> 10 USD/hr • Weighted average cost of all items -> 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 • @ $6.50 = $4,916 • @ $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 • alpha=1.71

  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 – b*Q • 7.00=a - b * 1400 • 6.50=a – b * 2800 • Solve two simultaneous linear equations • a= 7.49, b=0.000357

  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?

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