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Anettt [7]
3 years ago
14

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
Mathematics
1 answer:
Bess [88]3 years ago
4 0

Answer:

They would produce 14,400 packages of zetsy and the regular profit making would be $11,340.

Step-by-step explanation:

12-ounce

regular = 65%

mild = 35%

extra sharp zesty blend = 75%

extra sharp mild = 25%

8,100 mild for = $1.30

3,500 extra sharp = $1.50

cost blend and package = $0.30

regular sold = $1.8

zesty = $2.10

first we calculate the cost of each product

conversion Of  ounces to pounds:

1 pound = 16 ounces

regular cost:

12/16 pounds x 65% mild x $1.30

= 0.63375

12/16 pounds x 35% sharp x $1.50

= 0.39375‬

+ blend and package $0.30

total = $1.3275‬

contribution: $1.8 – $1.3275

= $0,4725‬

zesty cost:

12/16 pounds x 75% mild x $1.30

= 0.73125‬

12/16 pounds x 25% sharp x $1.50

= 0.28125‬

+ blend and package 0.30

total $1,3125‬

contribution: $2.10 – $1.3125

= $0,7875‬

to maximize profit:

profit = $0.4725Regular + $0.7875zetzy

adding the  constraint:

mild = Regular x $0.4775 + Zetzy x $0.5625 = 8,100

and

sharp = Regular x $0.2625 + Zetzy x $0.1875 = 3,100

contribution generated by each product/pound:

                                 Regular        Zesty

CM                          $ 0.47250 $ 0.47250

Constrain resource

( pounds of mild)         0.48750 0.56250

CM per constrain        $ 0.9692 $ 1.4000

Constrain resource

( pounds of sharp)         0.26250 0.18750

CM per constrain           $ 1.80      $ 4.20

As zesty is better we produce as much as we can:

8,100 pounts / 0.5625 per cheese spreads: 14,400

check for possibilities of other constraint:

14,400 zesty packages x 0.1875 pounds each = 2,700 pounds

because it’s possible we only produce zetsy

profit = $0.4725 (0) + $0.7875 (14,400)

profit =  $ 11,340

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