Optimal Quantity for Midwestern Hardware

What is the optimal quantity for Midwestern Hardware to order if the forecast calls for a 40% chance of a harsh winter?

  • The optimal quantity to order for Midwestern if the forecast calls for a 40% chance of a harsh winter is 3000.
  • The company must order 3000 shovels in anticipation of a harsh winter to maximize the expected payoff.

Calculating the Optimal Quantity

Given Data:
  • Cost of each shovel: $15.00
  • Selling price of each shovel: $29.95
  • Discount selling price of each shovel: $10.00
  • Probability of harsh winter: 40%
  • Probability of mild winter: 60%

Probability Distribution of Regular Price Demand:

  • Regular price demand: 250, 300, 350, 400, 450, 500, 550
  • Probabilities: 0.2, 0.3, 0.1, 0.1, 0.2, 0.05, 0.05

Calculation of Probability of Demand:

  • Various probabilities of demand for different quantities of shovels can be calculated based on the given data.

Payoff Table Construction:

  • Expected payoff is calculated by multiplying the probability with the difference between revenue and cost.
  • For Midwestern Hardware, expected payoffs for different order quantities can be calculated using the provided data.
  • The order quantity with the highest expected payoff is considered the optimal quantity to order.

Result:

  • The optimal quantity for Midwestern Hardware to order in anticipation of a 40% chance of a harsh winter is 3000 shovels.
  • This quantity maximizes the expected payoff and ensures the company is prepared for the potential demand during a harsh winter season.
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