1. The local supermarket buys lettuce each day to ensure really fresh produce. 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 a box. The lettuce is sold for $10.00 a box and the dealer that sells old lettuce is willing to pay $1.50 a box. Past history says that tomorrow's demand for lettuce is normally distributed with an average of 250 boxes and a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase tomorrow? 2. Sally's Silk Screening produces specialty T-shirts that are primarily sold at special events. She is trying to decide how many to produce for an upcoming event. During the event, Sally can sell I- shirts for $20 apiece. However, when the event ends, any unsold T-shirts are sold for $4 each. It costs Sally $8 to make a specialty T-shirt. Sally's estimate of demand is the following: Demand Probability 300 0.0 400 0.10 500 0.40 600 0.30 700 0.10 800 0.05 (a) What is the optimal service level? (b) How many T-shirts should she produce for the upcoming event? . Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are the specialty of his shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand, he estimates demand for cookies as the following Demand Probability of Demand 1,800 dozen 2,000 0.10 2,200 0.20 2,400 0.30 2,600 0.20 2,800 0.10 3,000 0.05 Each dozen sells for $0.69 and costs $0.49, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.29 and sold the following day as day-old merchandise. What is the optimal number of cookies to make? 4. Johnson Electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed twice every year. Each printing run incurs a fixed cost of $5,000, which involves catalog design cost and printing setup cost. The variable production cost is $5 per catalog. Annual demand for catalogs is estimated to be normally distributed with a mean of 16,000 and standard deviation of 4,000. Data indicate that, on average, each customer ordering a catalog generates a profit of $35 from sales. How many catalogs should be printed in each run