The New England Cheese Company produces two cheese spreads b

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

Solution

Regular has
.80*.75 = 0.6 lb mild
.20*.75 = 0.15 lb sharp

Zesty has
.60*.75 = 0.45 lb mild
.40*.75 = 0.3 lb sharp

Cost per container is:

R: 0.6*1.2 + 0.15*1.4 + 0.2 = 1.13
Z: 0.45*1.2 + 0.3*1.4 + 0.2 = 1.16

So, total profit is

P = R*(1.95 - 1.13) + Z*(2.20 - 1.16)

Constraints:
0.6*R + 0.45*Z <= 8100
0.15*R + 0.3*Z <= 9000