Question

The local supermarket buys lettuce each day to ensure really fresh products. Each morning, any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week, the supermarket can buy fresh lettuce for $4.00 per box. The lettuce is sold for $10.00 per box and the dealer that resells old lettuce is willing to pay $1.50 per box. Past history says that tomorrow's demand for lettuce is normally distributed with a mean of 250 boxes and a standard deviation of 34 boxes. a. How many boxes of lettuce should the supermarket purchase tomorrow? b. If the dealer is willing to pay $1 more for per box of old lettuce, will your answer in part (a) increase, decrease or stay unchanged? Please explain the practical intuition.

Answer 1

The supermarket should purchase approximately 306 boxes of lettuce tomorrow based on the normal distribution of demand. The answer in part (a) would likely stay unchanged if the dealer is willing to pay $1 more for old lettuce.

Step-by-step explanation:

To determine how many boxes of lettuce the supermarket should purchase tomorrow, we need to consider the demand for lettuce. The demand for lettuce is normally distributed with a mean of 250 boxes and a standard deviation of 34 boxes. The supermarket should purchase enough lettuce to meet the expected demand plus a safety stock. The safety stock is typically calculated based on a desired service level. Let's assume a service level of 95%, which corresponds to a z-score of 1.645. Therefore, the supermarket should purchase 250 + 1.645 * 34 = 305.93, or approximately 306 boxes of lettuce tomorrow.

If the dealer is willing to pay $1 more per box of old lettuce, the supermarket's answer in part (a) would likely stay unchanged. This is because the supermarket is focused on meeting the fresh lettuce demand, rather than relying heavily on selling old lettuce to the dealer. The decision to purchase fresh lettuce is based on the expected demand and the desire to provide fresh products to customers.