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16 December, 21:44

Problem 7-37 (Algorithmic) 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.

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  1. 16 December, 22:28
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    It will produce 14,400 packages of zesty and non opf the regular making a profit of $ 11,340

    Explanation:

    12-ounce

    regular 65% mild 35% extra sharp

    zesty blend 75% mild 25% extra sharp

    8,100 mild for 1.30

    3,500 extra sharp 1.50

    cost blend and package 0.30

    regular sold at 1.8

    zesty at 2.10

    We should calcualte the cost of each product and get the contribution per unit:

    conversion between ounces and 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

    We want to maximize profit:

    profit = 0.4725Regular + 0.7875zetzy

    With the constrain:

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

    and

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

    contribution generate per product and per 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

    we check if it is possible with the other constrain:

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

    it is possible therefore we only produce zesty

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

    profit = $ 11,340
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