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 80% mild cheddar and 20% extra sharp, and the Zesty blend contains 60% mild cheddar and 40% extra sharp. This year, a local dairy co-operative offered to provide up to 8100 pounds of mild cheddar cheese for $1.20 per pound and up to 3000 pounds of extra sharp cheddar cheese for $1.40 per pound. 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?

Explanation / Answer

Let R is the number of containers of Regular

Z is the number of containers of Zesty

Regular has

0.80*0.75=0.6lb mild

0.20*0.75=0.15 lb sharp

Zesty has

0.60*0.75=0.45lb mild

0.40*0.75=0.3lb 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

Total profit is given by

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

Principle constaints

0.60R+0.45Z <= 8100

0.15R +0.30Z<=3000

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