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Matrix Problem

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.

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