44. Cost Analysis The Mundo Candy Company makes three

types of chocolate candy: Cheery Cherry, Mucho Mocha,

and Almond Delight. The company produces its products

in San Diego, Mexico City, and Managua using two main

ingredients: chocolate and sugar.

a. Each kilogram of Cheery Cherry requires .5 kg of sugar

and .2 kg of chocolate; each kilogram of Mucho Mocha

requires .4 kg of sugar and .3 kg of chocolate; and each

kilogram of Almond Delight requires .3 kg of sugar

and .3 kg of chocolate. Put this information into a 2 X 3

matrix, labeling the rows and columns.

b. The cost of 1 kg of sugar is $4 in San Diego, $2 in Mexico

City, and $1 in Managua. The cost of 1 kg of chocolate

is $3 in San Diego, $5 in Mexico City, and $7 in

Managua. Put this information into a matrix in such a

way that when you multiply it with your matrix from

part a, you get a matrix representing the ingredient cost

of producing each type of candy in each city.

c. Multiply the matrices in parts a and b, labeling the product

matrix.

d. From part c, what is the combined sugar-and-chocolate

cost to produce 1 kg of Mucho Mocha in Managua?

e. Mundo Candy needs to quickly produce a special shipment

of 100 kg of Cheery Cherry, 200 kg of Mucho

Mocha, and 500 kg of Almond Delight, and it decides to

select one factory to fill the entire order. Use matrix multiplication

to determine in which city the total sugar-and chocolate

cost to produce the order is the smallest.

types of chocolate candy: Cheery Cherry, Mucho Mocha,

and Almond Delight. The company produces its products

in San Diego, Mexico City, and Managua using two main

ingredients: chocolate and sugar.

a. Each kilogram of Cheery Cherry requires .5 kg of sugar

and .2 kg of chocolate; each kilogram of Mucho Mocha

requires .4 kg of sugar and .3 kg of chocolate; and each

kilogram of Almond Delight requires .3 kg of sugar

and .3 kg of chocolate. Put this information into a 2 X 3

matrix, labeling the rows and columns.

b. The cost of 1 kg of sugar is $4 in San Diego, $2 in Mexico

City, and $1 in Managua. The cost of 1 kg of chocolate

is $3 in San Diego, $5 in Mexico City, and $7 in

Managua. Put this information into a matrix in such a

way that when you multiply it with your matrix from

part a, you get a matrix representing the ingredient cost

of producing each type of candy in each city.

c. Multiply the matrices in parts a and b, labeling the product

matrix.

d. From part c, what is the combined sugar-and-chocolate

cost to produce 1 kg of Mucho Mocha in Managua?

e. Mundo Candy needs to quickly produce a special shipment

of 100 kg of Cheery Cherry, 200 kg of Mucho

Mocha, and 500 kg of Almond Delight, and it decides to

select one factory to fill the entire order. Use matrix multiplication

to determine in which city the total sugar-and chocolate

cost to produce the order is the smallest.

## This question was asked on Apr 17, 2010.

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