The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 2 pound containers, which are then sold to distributors throughout the Northeast. The Regular blend must at least 20% extra sharp cheddar, and the Zesty blend must contain at least 25% extra sharp cheddar. The company has orders for 3500 containers of Regular and 4500 containers of Zesty.
This year, a local dairy cooperative offered to provide up to 8100 pounds of cheese blend 1 for $1.20 per pound and up to 9000 pounds of cheese blend 2 for $1.40 per pound. Cheese blend 1 consists of 90% mild cheddar and 10% extra sharp while cheese blend 2 consists of 65% mild and 35% extra sharp.
The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.20 per container. If each container of Regular is sold for $1.95 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce? Formulate a Linear Programming model to determine these amounts