Question

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 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 85% mild cheddar and 15% extra sharp, and the Zesty blend contains 75% mild cheddar and 25% extra sharp. This year, a local dairy cooperative offered to provide up to 9,000 pounds of mild cheddar cheese for $1.50 per pound and up to 4,000 pounds of extra sharp cheddar cheese for $1.70 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.25 per container. If each container of Regular is sold for $2.00 and each container of Zesty is sold for $2.50, how many containers of Regular and Zesty should New England Cheese produce?

Do not round your interim computations. If required, round your answers to the nearest whole number.

Let R=		number of containers of Regular
Z =		number of containers of Zesty

Optimal Solution: R =  , Z =  , profit = $ .

Answer 1

Optimal Solution: R = 0, Z = 16000, Profit = $ 17,400

Algebraic formulation

Decision Variable: Let R, Z be the number of containers of Regular and Zesty blend respectively that New England Cheese should produce.

Objective function: Maximize Profit:     0.603*R + 1.088*Z

Subject to constraints:

(0.85R + 0.75Z)*12/16 ≤ 9000                                                                                                     

(0.15R + 0.25Z)*12/16 ≤ 4000                                                                                                     

R, Z ≥ 0