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 containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 9.6 ounces of mild cheddar and 2.4 ounces of extra sharp, and the Zesty blend contains 7.2 ounces of mild cheddar and 4.8 ounces of extra sharp. This year, a local dairy cooperative offered to provide up to 129600 ounces of mild cheddar cheese and up to 48000 ounces of extra sharp cheddar cheese. The regular blend costs $0.93 per container and the Zesty blend costs $0.96 per container. The cost to blend and package the cheese spreads, excluding the cost of the cheese blend, is $0.20 per container. Each container of Regular is sold for $1.95 and each container of Zesty is sold for $2.20. [Hint: Profit = Revenue - Cost] (a) Formulate a linear optimization model that will enable New England Cheese to determine containers of Regular and Zesty products that will maximize the total profit contribution. (b) What are the optimal production quantities? (c) Formulate the dual of the standard linear optimization model in part (a). (d) What are the dual prices for each constraint? Interpret each.
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
containers, which are then sold to distributors throughout the Northeast. The Regular
blend contains 9.6 ounces of mild cheddar and 2.4 ounces of extra sharp, and the
Zesty blend contains 7.2 ounces of mild cheddar and 4.8 ounces of extra sharp. This
year, a local dairy cooperative offered to provide up to 129600 ounces of mild cheddar
cheese and up to 48000 ounces of extra sharp cheddar cheese. The regular blend costs
$0.93 per container and the Zesty blend costs $0.96 per container. The cost to blend
and package the cheese spreads, excluding the cost of the cheese blend, is $0.20 per
container. Each container of Regular is sold for $1.95 and each container of Zesty is
sold for $2.20.
[Hint: Profit = Revenue - Cost]
(a) Formulate a linear optimization model that will enable New England Cheese
to determine containers of Regular and Zesty products that will maximize the total
profit contribution.
(b) What are the optimal production quantities?
(c) Formulate the dual of the standard linear optimization model in part (a).
(d) What are the dual prices for each constraint? Interpret each.
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