Question

An order is received for 400 loaves of whole wheat bread, 200 loaves of oat bread, and 350 loaves of rye bread. Given that the cost of mixing, baking, and packaging is $14, $25, and$2, respectively, per hour, find matrices B and C so that the product BAC will give the total cost (excluding raw materials) of filling this order. Find the total cost.

Answer 1

Final cost = $ 1313

Explanation:

Solution:-

- The order details for number of loaves for each type of bread are as follows:

{ 400 whole wheat , 200 oat bread . 350 rye bread }

- The cost per hour of mixing, baking, and packaging is as follows:

{ $ 14 , $ 25 , $ 2 }

- The time taken in hours for making each bread in terms of mixing, backing and packaging is given in a form of matrix:

`A = \left[\begin{array}{cccc}Mix&Bake&Package\\0.04&0.07&0.02&Wheat\\0.03&0.05&0.02&Oat\\0.04&0.06&0.02&Rye\end{array}\right]`

- We will define matrix B as the number of each bread on order. Such that AB gives us the time taken for making order:

`B = \begin{array}{ccc}400\\200\\350\end{array}`

- The product of two matrix AxB would be:

`A*B = \left[\begin{array}{cccc}Mix&Bake&Package\\0.04&0.07&0.02&Wheat\\0.03&0.05&0.02&Oat\\0.04&0.06&0.02&Rye\end{array}\right] x \left[\begin{array}{ccc}400\\200\\350\end{array}\right] = \left[\begin{array}{ccc}37\\29\\35\end{array}\right]`

- The matrix C representing the rates:

`C = \left[\begin{array}{ccc}14&25&2\end{array}\right]`

- The final cost would be:

`\left[\begin{array}{ccc}14&25&2\end{array}\right] x \left[\begin{array}{ccc}37\\29\\35\end{array}\right] = 1313`

Final cost = $ 1313