Linear Programming

-Song Company produces two types of HDTV’s:   LCD and Plasma. They have agreed to deliver 5000 units of LCD’s in month 1 and 8000 units in month 2. For plasma’s, the agreement is 2000 units in month 1 and 4000 units in month 2. S-Song has two plants, one in Seoul and one in Busan. The available production hours and production rate for the products are given in the following table.     Busan Seoul Production Hours     Month 1 800 2000 Month 2 400 1200 Production Rate in hours     LCD 0.15 0.16 Plasma 0.12 0.14     It costs $5,000 per hour of plant time to produce any product in either plant. The inventory carrying cost per month for each product is $200 per unit (charged on each month’s ending inventory). At present, there are 500 units of LCD’s and 750 units of Plasma’s in inventory. Formulate and solve an LP to determine the production schedule that minimizes the total cost incurred in meeting demand. Problem 2 Juiceco manufactures two products: premium orange juice and regular orange juice.  Both products are made by combining two types of oranges: grade 6 and grade 3.  The oranges in premium juice must have an average grade of at least 5, those in regular juice at least 4.  During each of the next two months Juiceco can sell up to 1000 gallons of premium juice and up to 2000 gallons of regular juice.  Premium juice sells for $1.00 per gallon, while regular juice sells for $0.80 per gallon.  At the beginning of month 1 Juiceco has 3000 gallons of grad 6 oranges and 2000 gallons of grade 3 oranges.  At the beginning of month 2 Juiceco may purchase additional grade 3 oranges for $0.40 per gallon and additional grade 6 oranges for $0.60 per gallon.  Juice spoils at the end of the month, so it makes no sense to make extra juice during month 1 in the hopes of using to meet month 2 demand.  Oranges left at the end of month 1 may be used to produce juice for month 2.  At the end of month 1 a holding cost of $0.05 is assessed against each gallon…