The New England Cheese Company produces two cheese spreads by blending mild ched

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 75% mild cheddar and 25% extra sharp, and the Zesty blend contains 70% mild cheddar and 30% extra sharp. This year, a local dairy cooperative offered to provide up to 8,500 pounds of mild cheddar cheese for $1.40 per pound and up to 2,700 pounds of extra sharp cheddar cheese for $1.60 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.40 per container. If each container of Regular is sold for $2.20 and each container of Zesty is sold for $2.80, how many containers of Regular and Zesty should New England Cheese produce? Do not round intermediate calculations. 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 = $  .

Explanation / Answer

Solution:

Each containers has 12 ounce = 0.75 lb

Regular Blend has

0.75*0.75 = 0.5625 lb mild chedder

0.25*0.75 = 0.1875 lb extra sharp

Zesty has

0.70 * 0.75 = 0.525 lb mild chedder

0.30 * 0.75 = 0.225 lb extra sharp

Cost per container of regular R

R = 0.5625*1.4 + 0.1875*1.6 +0.4 = 1.4875

Cost per container of Zesty Z

Z = 0.525 * 1.4 + 0.225 *1.6 +0.4 = 1.495   

Profit

= R* (2.20 -1.4875) + Z*(2.80-1.495)

Answer

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