MATH138a – QUANTITATIVE TECHNIQUES IN BUSINESS
PROBLEM SET: FINAL PERIOD

Direction: Solve the following problems. Write your complete solution for full or partial credit.

1. Ben’s Muffler Repair advertises that it is able to replace a car muffler on the same day a customer brings a car into the shop. If for any reason Ben cannot keep his promise, he pays the customer $100. Ben has found that for LN-70 mufflers, the optimal reorder quantity is 30 mufflers; he orders LN-70 mufflers 10 times a year. As LN-70 mufflers have to be ordered from a manufacturer located a considerable distance away, lead time for his orders is 30 working days, a period of time in which Ben on the average sells 30 LN-70 mufflers. During the past 10 years, 100 orders were placed. There were 10 occasions when Ben sold 32 LN-70s, 5 occasions when he sold 35 and only 1 when he sold 36 during the 30-day order period. On each of the other 84 occasions, he sold 30 or fewer. If it costs Ben $18 a year to hold one LN-70 in safety stock, what should Ben establish as his reorder point for LN-70 mufflers to minimize his costs? At this level of safety stock, how many $100 bills will Ben expect to give to car owners whose cars require an LN-70 muffler?

2. A toy company produces two types of toy model cars, Star Platinum and Greenlight Bullitt models. Three machines are required are required to produce each type; these machines are classified as X, Y, and Z. Each Star Platinum requires 7 minutes of process time in machine X, 4 minutes on machine Y, and 10 minutes on machine Z. A Greenlight Bullitt requires 4 minutes on X, 15 minutes on Y, and 16 minutes on Z. Each day there are 420 minutes available on machine X, 600 minutes on machine Y, and 840 minutes on machine Z. The variable costs are $10 per unit for Star Platinum and $14 per unit for the Greenlight Bullitt. Star Platinum sell at a price of