Expert: Steve Holleran - 11/27/2007

Question
I cant figure out how to do this, I will write out the whole thing, you have to use matrixes to solve it:
  A candy company packages caramels, chocolates, and hard candy in three different assortments: traditional, delux, and superb. For each type of candy the table below gives the number in each assortment, the number of Calories per piece, and the cost to make each piece.

    traditional  delux   superb   Calories      Cost per           -                                 per piece    piece(cents)
caramels 10         16     15           60          10
chocolates 12       8       25          70          12
card candy 10       16      8           55           6

  The company recieves an order for 300 traditional, 180 delux and 100 superb assortments.

1. Find the number of each type of candy needed to fill the order.

2. Find the total number of calories in each type of assortment.

3. Find the cost of production for each type of assortment.

4. Find the cost to fill the order.

    Thank you so much!   -  

Answer
Hi Samantha,

Well, there's a lot of information here, and its not easy to show some of the matrices using script, but let's try:

1.  For the number of each type, make a column matrix (3 by 1)
for each assortment:

 T = [10         D = [ 16             S = [15

      12                8                  25

      12]              16]                  8]

To fill the order, you need

   300[T] + 180[D] + 100[S] = [7380  Caramel

                               7540  Chocolate

                               6680] Hard Candy

2.  For the total calories in each assortment, for each type of assortment multiply a 1 by 3 matrix of the calories by a 3 by 1 matrix of the candies:

Traditional :  [60  70  55] * [10

                              12

                              10]

to do this, you do :  60 * 10 + 70 * 12 + 55 * 10 = 1990

You do the same for the Deluxe and Superb, just replace the column matrix above with the column matrix for each of those.

So, for Deluxe, you would have : 60 * 16 + 70 * 8 + 55 * 16 = 2400

And for Superb, you would have : 60 * 15 + 70 * 25 + 55 * 8 = 3090

3.  For the cost, you have these multiplications:

Traditional:  [10   * [10   12  6]

               12

               10]

 Deluxe:      [16   *  [10   12   6]

                8

               16]


Superb:        [15     *  [10    12    6]

               25

               8]


4.  Then, for the cost of the order, you have

  [3600   *  [ 10   12   6]

   3600

   3000]

This comes to a total of $97,200.

Sorry it took me so long, but its not easy to represent these matrices.  Hope you can understand the operations.

Steve