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.

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