Problem 7-37 The New England Cheese Company produces two cheese spreads by blend
ID: 2621619 • Letter: P
Question
Problem 7-37
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?
Problem 7-37
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?
Let R = number of containers of Regular Z = number of containers of ZestyOptimal Solution: R = , Z = , profit = $ .
Explanation / Answer
Originally posted by Petruchio:
In your constraints you forgot that each container is .75 lb
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 <= 3000