question archive The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese
The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese
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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 65% mild cheddar and 35% 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 8100 pounds of mild cheddar cheese for $1.30 per pound and up to 3500 pounds of extra sharp cheddar cheese for $1.50 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.30 per container. If each container of Regular is sold for $1.80 and each container of Zesty is sold for $2.10, 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 = $ .
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Answer:
Let R= number of containers of Regular
Z =number of containers of Zesty.
Note that, as the containers are of 12 ounces so,
Cost to produce Regular cheese spreads per container = (0.65*$1.30+0.35*$1.50)*0.75+$0.30
= $1.3275
Cost to produce Zesty cheese spreads per container = (0.75*$1.30+0.25*$1.50) *0.75+$0.30
= $1.3125
Then the LPP can be formulated as follows,
Maximize P = $(1.80-1.3275)*R + $(2.10-1.3125)*Z
Subject to,
0.65*0.75*R + 0.75*0.75*Z ≤ 8100
0.35*0.75*R + 0.25*0.75*Z ≤ 3500
R, Z ≥ 0
This can be rewritten as,
Maximize P = 0.4725*R + 0.7875*Z
Subject to,
0.4875*R + 0.5625*Z ≤ 8100
0.2625*R + 0.1875*Z ≤ 3500
R, Z ≥ 0
Using the solver found at http://simplex.tode.cz/
Optimal Solution: R = 0 , Z = 14400, profit = $11340.
