Amanufacturing company receives orders for engines from two assembly plants. plant i needs at least 45 engines, and plant ii needs at least 32 engines. the company can send at most 140 engines to these assembly plants. it costs $30 per engine to ship to plant i and $40 per engine to ship to plant ii. plant i gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant ii gives similar $10 rebates. the manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. how many engines should be shipped to each plant to minimize shipping costs? what is the minimum cost?

Haley photocopying purchases a paper from an out-of-state vendor. average weekly demand for paper is 150 cartons per week for which haley pays $15 per carton. in bound shipments from the vendor average 1000 cartoons with an average lead time of 3 weeks. haley operates 52 weeks per year; it carries a 4-week supply of inventory as safety stock and no anticipation inventory. the vendor has recently announced that they will be building a faculty near haley photocopying that will reduce lead time to one week. further, they will be able to reduce shipments to 200 cartons. haley believes that they will be able to reduce safety stock to a 1-week supply. what impact will these changes make to haley’s average inventory level and its average aggregated inventory value?