Question

A local farm market buys fresh fruits and vegetables from local farmers. It buys peaches from one farmer at a cost of $1.00 per pound and sells them for $2.00 per pound. The demand for peaches during the season is normally distributed with a mean of 40 pounds per day and a daily standard deviation of 6 pounds. At the end of each business day, any unsold peaches are purchased by local restaurants for $0.40 per pound (in U.S. dollars): Enter your answers to one decimal place. Determine the service level. The service level is Number %. What is the optimal stocking level for the service level deterimined in (a)

Answer 1

1. The service level is 63%

2. 42 pounds

Step-by-step explanation:

1. Cost Price of Peaches = $1.00 per pound

Selling Price of Peaches = $2.00 per pound

Cost of shortage = Selling Price of Peaches - Cost Price of Peaches = $2 - $1 = $1

Cost of overage = Cost Price of Peaches - salvage value = $1 - $0.4 = $0.6

Service level = Cost of shortage /(Cost of shortage + Cost of overage)

= $1/($1 + $0.6) = $1/$1.6 =0.625 = 62.5% ≈ 63%

The service level is 63%

2. The z value for this service level = 0.332

Mean = 40 pounds

Standard deviation = 6 pounds

Optimum stocking level = (Mean + z value x Standard deviation)

= 40 + 6 × 0.332 = 41.992 ≈ 42 pounds

The optimal stocking level for the service level deterimined in (a) is 42 pounds